1.4: Engagement in a Democracy
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Learning Objectives
By the end of this section, you will be able to:
- Explain the importance of citizen engagement in a democracy
- Describe the main ways Americans can influence and become engaged in government
- Discuss factors that may affect people’s willingness to become engaged in government
Participation in government matters. Although people may not get all that they want, they can achieve many goals and improve their lives through civic engagement. According to the pluralist theory, government cannot function without active participation by at least some citizens. Even if we believe the elite make political decisions, participation in government through the act of voting can change who the members of the elite are.
Why Get Involved?
Are fewer people today active in politics than in the past? Political scientist Robert Putnam has argued that civic engagement is declining; although many Americans may report belonging to groups, these groups are usually large, impersonal ones with thousands of members. People who join groups such as Amnesty International or Greenpeace may share certain values and ideals with other members of the group, but they do not actually interact with these other members. These organizations are different from the types of groups Americans used to belong to, like church groups or bowling leagues. Although people are still interested in volunteering and working for the public good, they are more interested in either working individually or joining large organizations where they have little opportunity to interact with others. Putnam considers a number of explanations for this decline in small group membership, including increased participation by women in the workforce, a decrease in the number of marriages and an increase in divorces, and the effect of technological developments, such as the internet, that separate people by allowing them to feel connected to others without having to spend time in their presence. 23
Putnam argues that a decline in social capital—“the collective value of all ‘social networks’ [those whom people know] and the inclinations that arise from these networks to do things for each other”—accompanies this decline in membership in small, interactive groups. 24 Included in social capital are such things as networks of individuals, a sense that one is part of an entity larger than oneself, concern for the collective good and a willingness to help others, and the ability to trust others and to work with them to find solutions to problems. This, in turn, has hurt people’s willingness and ability to engage in representative government. If Putnam is correct, this trend is unfortunate, because becoming active in government and community organizations is important for many reasons.
Some have countered Putnam’s thesis and argue that participation is in better shape than what he portrays. Everett Ladd shows many positive trends in social involvement in American communities that serve to soften some of the declines identified by Putnam. For example, while bowling league participation is down, soccer league participation has proliferated. 25 April Clark examines and analyzes a wide variety of social capital data trends and disputes the original thesis of erosion. 26 Others have suggested that technology has increased connectedness, an idea that Putnam himself has critiqued as not as deep as in-person connections. 27
Link to Learning
To learn more about political engagement in the United States, read “The Current State of Civic Engagement in America” by the Pew Research Center.
Civic engagement can increase the power of ordinary people to influence government actions. Even those without money or connections to important people can influence the policies that affect their lives and change the direction taken by government. U.S. history is filled with examples of people actively challenging the power of elites, gaining rights for themselves, and protecting their interests. For example, slavery was once legal in the United States and large sectors of the U.S. economy were dependent on this forced labor. Slavery was outlawed and blacks were granted citizenship because of the actions of abolitionists. Although some abolitionists were wealthy white men, most were ordinary people, including men and women of both races. White women and blacks were able to actively assist in the campaign to end slavery despite the fact that, with few exceptions, they were unable to vote. Similarly, the right to vote once belonged solely to white men until the Fifteenth Amendment gave the vote to African American men. The Nineteenth Amendment extended the vote to include women, and the Voting Rights Act of 1965 made exercising the right to vote a reality for African American men and women in the South. None of this would have happened, however, without the efforts of people who marched in protest, participated in boycotts, delivered speeches, wrote letters to politicians, and sometimes risked arrest in order to be heard (Figure 1.8). The tactics used to influence the government and effect change by abolitionists and members of the women’s rights and African American civil rights movements are still used by many activists today.
The rights gained by these activists and others have dramatically improved the quality of life for many in the United States. Civil rights legislation did not focus solely on the right to vote or to hold public office; it also integrated schools and public accommodations, prohibited discrimination in housing and employment, and increased access to higher education. Activists for women’s rights fought for, and won, greater reproductive freedom for women, better wages, and access to credit. Only a few decades ago, homosexuality was considered a mental disorder, and intercourse between consenting adults of the same sex was illegal in many states.
Activism can improve people’s lives in less dramatic ways as well. Working to make cities clean up vacant lots, destroy or rehabilitate abandoned buildings, build more parks and playgrounds, pass ordinances requiring people to curb their dogs, and ban late-night noise greatly affects people’s quality of life. The actions of individual Americans can make their own lives better and improve their neighbors’ lives as well.
Representative democracy cannot work effectively without the participation of informed citizens, however. Engaged citizens familiarize themselves with the most important issues confronting the country and with the plans different candidates have for dealing with those issues. Then they vote for the candidates they believe will be best suited to the job, and they may join others to raise funds or campaign for those they support. They inform their representatives how they feel about important issues. Through these efforts and others, engaged citizens let their representatives know what they want and thus influence policy. Only then can government actions accurately reflect the interests and concerns of the majority. Even people who believe the elite rule government should recognize that it is easier for them to do so if ordinary people make no effort to participate in public life.
Pathways to Engagement
People can become civically engaged in many ways, either as individuals or as members of groups. Some forms of individual engagement require very little effort. One of the simplest ways is to stay informed about debates and events in the community, in the state, and in the nation. Awareness is the first step toward engagement. News is available from a variety of reputable sources, such as newspapers like the New York Times ; national news shows, including those offered by the Public Broadcasting Service and National Public Radio; and reputable internet sites.
Another form of individual engagement is to write or email political representatives. Filing a complaint with the city council is another avenue of engagement. City officials cannot fix problems if they do not know anything is wrong to begin with. Responding to public opinion polls, actively contributing to a political blog, or starting a new blog are all examples of different ways to be involved.
One of the most basic ways to engage with government as an individual is to vote (Figure 1.9). Individual votes do matter. City council members, mayors, state legislators, governors, and members of Congress are all chosen by popular vote. Although the president of the United States is not chosen directly by popular vote but by a group called the Electoral College, the votes of individuals in their home states determine how the Electoral College ultimately votes. Registering to vote beforehand is necessary in most states, but it is usually a simple process, and many states allow registration online. (We discuss voter registration and voter turnout in more depth in a later chapter.)
Voting, however, is not the only form of political engagement in which people may participate. Individuals can engage by attending political rallies, donating money to campaigns, and signing petitions. Starting a petition of one’s own is relatively easy, and some websites that encourage people to become involved in political activism provide petitions that can be circulated through email. Taking part in a poll or survey is another simple way to make your voice heard.
Milestone
Votes for Eighteen-Year-Olds
Young Americans are often reluctant to become involved in traditional forms of political activity. They may believe politicians are not interested in what they have to say, or they may feel their votes do not matter. However, this attitude has not always prevailed. Indeed, today’s college students can vote because of the activism of college students in the 1960s. Most states at that time required citizens to be twenty-one years of age before they could vote in national elections. This angered many young people, especially young men who could be drafted to fight the war in Vietnam. They argued that it was unfair to deny eighteen-year-olds the right to vote for the people who had the power to send them to war. As a result, the Twenty-Sixth Amendment, which lowered the voting age in national elections to eighteen, was ratified by the states and went into effect in 1971.
Are you engaged in or at least informed about actions of the federal or local government? Are you registered to vote? How would you feel if you were not allowed to vote until age twenty-one?
Some people prefer to work with groups when participating in political activities or performing service to the community. Group activities can be as simple as hosting a book club or discussion group to talk about politics. Coffee Party USA provides an online forum for people from a variety of political perspectives to discuss issues that are of concern to them. People who wish to be more active often work for political campaigns. Engaging in fundraising efforts, handing out bumper stickers and campaign buttons, helping people register to vote, and driving voters to the polls on Election Day are all important activities that anyone can engage in. Individual citizens can also join interest groups that promote the causes they favor.
Get Connected!
Getting Involved
In many ways, the pluralists were right. There is plenty of room for average citizens to become active in government, whether it is through a city council subcommittee or another type of local organization. Civic organizations always need volunteers, sometimes for only a short while and sometimes for much longer.
For example, Common Cause is a non-partisan organization that seeks to hold government accountable for its actions. It calls for campaign finance reform and paper verification of votes registered on electronic voting machines. Voters would then receive proof that the machine recorded their actual vote. This would help to detect faulty machines that were inaccurately tabulating votes or election fraud. Therefore, one could be sure that election results were reliable and that the winning candidate had in fact received the votes counted in their favor. Common Cause has also advocated that the Electoral College be done away with and that presidential elections be decided solely on the basis of the popular vote.
Follow-up activity: Choose one of the following websites to connect with organizations and interest groups in need of help:
- Common Cause ;
- Friends of the Earth which mobilizes people to protect the natural environment;
- Grassroots International which works for global justice;
- The Committee for a Responsible Federal Budget which seeks to inform the public on issues with fiscal impact and favors smaller budget deficits; or
- Conservative Leaders For Education which supports local control and increased parent choice in education.
Political activity is not the only form of engagement, and many people today seek other opportunities to become involved. This is particularly true of young Americans. Although young people today often shy away from participating in traditional political activities, they do express deep concern for their communities and seek out volunteer opportunities. 28 Although they may not realize it, becoming active in the community and engaging in a wide variety of community-based volunteer efforts are important forms of civic engagement and help government do its job. The demands on government are great, and funds do not always exist to enable it to undertake all the projects it may deem necessary. Even when there are sufficient funds, politicians have differing ideas regarding how much government should do and what areas it should be active in. Volunteers and community organizations help fill the gaps. Examples of community action include tending a community garden, building a house for Habitat for Humanity, cleaning up trash in a vacant lot, volunteering to deliver meals to the elderly, and tutoring children in after-school programs (Figure 1.10).
Some people prefer even more active and direct forms of engagement such as protest marches and demonstrations, including civil disobedience. Such tactics were used successfully in the African American civil rights movement of the 1950s and 1960s and remain effective today. Likewise, the sit-ins (and sleep-ins and pray-ins) staged by African American civil rightsactivists, which they employed successfully to desegregate lunch counters, motels, and churches, have been adopted today by movements such as Black Lives Matter and Occupy Wall Street (Figure 1.11). Other tactics, such as boycotting businesses of whose policies the activists disapproved, are also still common. Along with boycotts, there are now “buycotts,” in which consumers purchase goods and services from companies that give extensively to charity, help the communities in which they are located, or take steps to protect the environment.
Link to Learning
Many ordinary people have become political activists. Read “19 Young Activists Changing America” to learn about people who are working to make people’s lives better.
Insider Perspective
Ritchie Torres
In 2013, at the age of twenty-five, Ritchie Torres became the youngest member of the New York City Council and the first gay council member to represent the Bronx (Figure 1.12). Torres became interested in social justice early in his life. He was raised in poverty in the Bronx by his mother and a stepfather who left the family when Torres was twelve. The mold in his family’s public housing apartment caused him to have asthma as a child, and he spent time in the hospital on more than one occasion because of it. His mother’s complaints to the New York City Housing Authority were largely ignored. In high school, Torres decided to become a lawyer, participated in mock trials, and met a young and aspiring local politician named James Vacca. After graduation, he volunteered to campaign for Vacca in his run for a seat on the City Council. After Vacca was elected, he hired Torres to serve as his housing director to reach out to the community on Vacca’s behalf. While doing so, Torres took pictures of the poor conditions in public housing and collected complaints from residents. In 2013, Torres ran for a seat on the City Council himself and won. In November 2020, Torres was elected to the U.S. House of Representatives to represent New York's 15th congressional district. He and Mondaire Jones, who represents NY 17, are the first openly gay Black men elected to Congress. He remains committed to improving housing for the poor. 29
Why don’t more young people run for local office as Torres did? What changes might they effect in their communities if they were elected to a government position?
Factors of Engagement
Many Americans engage in political activity on a regular basis. A survey conducted in 2008 revealed that approximately two-thirds of American adults had participated in some type of political action in the past year. These activities included largely non-personal activities that did not require a great deal of interaction with others, such as signing petitions, contacting elected representatives, or contributing money to campaigns. During the same period, approximately 30 percent of people attended a local government meeting or a political rally or event, while 16 percent worked or volunteered for a campaign. 30
Americans aged 18–29 were less likely to become involved in traditional forms of political activity than older Americans. A 2018 poll of more than two thousand young adults by Harvard University’s Institute of Politics revealed that only 24 percent claimed to be politically engaged, and fewer than 35 percent said that they had voted in a primary. Only 9 percent said that they had gone to a political demonstration, rally, or march. 31 However, in the 2018 midterm elections, an estimated 31 percent of Americans under thirty turned out to vote, the highest level of young adult engagement in decades. 32 In 2020, Harvard's polling showed significant interest in the 2020 presidential campaign and intent to vote. Post-election analysis by Tuft University's Center for Information and Research on Civic Learning & Engagement (CIRCLE) showed a record youth turnout of 53 percent, which was greater even than the historic turnout in the 2008 contest. The young vote swung heavily toward Biden in swing states. And, yet, young voters again participated at lower rates than did other age groups. 33
Why are younger Americans less likely to become involved in traditional political organizations? One answer may be that as American politics become more partisan in nature, young people turn away. Committed partisanship, which is the tendency to identify with and to support (often blindly) a particular political party, alienates some Americans who feel that elected representatives should vote in support of the nation’s best interests instead of voting in the way their party wishes them to. When elected officials ignore all factors other than their party’s position on a particular issue, some voters become disheartened while others may become polarized. However, a recent study reveals that it is a distrust of the opposing party and not an ideological commitment to their own party that is at the heart of most partisanship among voters. 34
Young Americans are particularly likely to be put off by partisan politics. More Americans under the age of thirty now identify themselves as Independents instead of Democrats or Republicans (Figure 1.13). Instead of identifying with a particular political party, young Americans are increasingly concerned about specific issues, such as same-sex marriage. 35 People whose votes are determined based on single issues are unlikely to vote according to party affiliation.
The other factor involved in low youth voter turnout in the past was that younger Americans did not feel that candidates generally tackle issues relevant to their lives. When younger voters cannot relate to the issues put forth in a campaign, such as entitlements for seniors, they lose interest. This dynamic changed somewhat in 2016 as Democratic candidate Bernie Sanders made college costs an issue, even promising free college tuition for undergraduates at public institutions. Senator Sanders enjoyed intense support on college campuses across the United States. After his nomination campaign failed, this young voter enthusiasm faded. Despite the fact that Democratic nominee Hillary Clinton eventually took up the free tuition issue, young people did not flock to her as well as they had to Sanders. In the general election, won by Republican nominee Donald Trump, turnout was down and Clinton received a smaller proportion of the youth vote than President Obama had in 2012. 36 In 2020, youth again felt connected with candidates, and that compelled participation throughout the election year. Sanders again galvanized interest, as did Biden and Harris during the general election phase. Student loan debt was a key campaign issue.
While some Americans disapprove of partisanship in general, others are put off by the ideology—established beliefs and ideals that help shape political policy—of one of the major parties. This is especially true among the young. While ideological polarization has occurred on both sides of the political spectrum, as some members of the Republican Party have become more ideologically conservative (e.g., opposing same-sex marriage, legalization of certain drugs, immigration reform, gun control, separation of church and state, and access to abortion), those young people who do identify with one of the major parties have in recent years tended to favor the Democratic Party. 37 Of the Americans under age thirty who were surveyed by Harvard in 2015, more tended to hold a favorable opinion of Democrats in Congress than of Republicans, and in the 2020 election, 61 percent of younger voters voted for the Democratic ticket (Figure 1.13). Even those young Americans who identify themselves as Republicans are more liberal on certain issues, such as being supportive of same-sex marriage and immigration reform, than are older Republicans. The young Republicans also may be more willing to see similarities between themselves and Democrats. 38 Once again, support for the views of a particular party does not necessarily mean that someone will vote for members of that party.
Other factors may keep even those college students who do wish to vote away from the polls. Because many young Americans attend colleges and universities outside of their home states, they may find it difficult to register to vote. In places where a state-issued ID is required, students may not have one or may be denied one if they cannot prove that they paid in-state tuition rates. 39
The likelihood that people will become active in politics also depends not only on age but on such factors as wealth and education. In 2020, as was the case in past elections, the percentage of people who reported that they were regular voters grew as levels of income and education increased. 40 , 41 Political involvement also depends on how strongly people feel about current political issues. Unfortunately, public opinion polls, which politicians may rely on when formulating policy or deciding how to vote on issues, capture only people’s latent preferences or beliefs. Latent preferences are not deeply held and do not remain the same over time. They may not even represent a person’s true feelings, since they may be formed on the spot when someone is asked a question about which they have no real opinion. Indeed, voting itself may reflect merely a latent preference because even people who do not feel strongly about a particular political candidate or issue vote. On the other hand, intense preferences are based on strong feelings regarding an issue that someone adheres to over time. People with intense preferences tend to become more engaged in politics; they are more likely to donate time and money to campaigns or to attend political rallies. The more money that one has and the more highly educated one is, the more likely one will form intense preferences and take political action. 42


11.2: Deception and Gaslighting
Defining Deception
Have you ever found yourself in a situation where you chose to tell a lie? Perhaps you were late to a meeting and blamed the traffic when really you just didn’t get ready in time. Maybe you found yourself telling someone they looked nice in an outfit even though you thought the outfit wasn’t suitable for them.  In what contexts do you feel it is acceptable to tell someone something other than the truth?
The first concept we will explore in the dark side of communication is the idea of deception . Whether or not you think it is OK to deceive someone probably includes consideration of what is at stake to you in terms of the risk to your relationship. This will determine whether or not you see any level of deception as acceptable to engage in for that particular relationship.
What do you think this means in a relationship when a relational partner decides to deceive someone? This theory focuses on how and why people engage in deception and try to get away with it and how the other person tries to figure out whether or not to believe it. Recall a time when you lied and someone questioned whether you were telling the truth. How did you respond? Or consider a time when you thought someone lied to you—how did you react and how did they respond back to you? Usually, when someone tries to deceive us and we are trying to figure out what is going on, we monitor our responses to figure out what to do next.
Whether or not a relationship can overcome deception really depends on that interplay between how someone responds when faced with deception and how the deceiver responds back in order to repair the relationship. In this next section, we will overview the types of deception.
Types of Deception
Let’s identify the different types of deception that might occur in a relationship: deception by omission (concealment) and deception by commission (lying) . These two types of deception differ according to the level of distortion that is involved and how much potential impact there is on a relationship because of how this deception is perceived.
Deception by Omission
Concealment , or deception by omission , involves intentionally holding back some of the information another person has requested, or you are expected to share. For example, a relational partner might ask why you didn’t respond to their text last night and you could say you were busy, while leaving out who you were busy with. Do you think lies by omission are detrimental to a relationship? What might happen if your relational partner finds out you have held back some information? Omitting information can violate relational expectations and can have an impact on the trust and intimacy that was already built in the relationship. As discussed in the chapter on building and maintaining interpersonal relationships, building trust is an important aspect of our relationships and we engage in self-disclosure and communication behaviors that help to build such trust. If our relational partners find out that we have violated their expectations of trust and undermined it through deception by omission, the trust in the relationship will automatically decline.
Deception by Commission
Simply put, this is lying . When we commit deception by commission , we deliberately communicate false information. This type of deception goes beyond just a strategic withholding of information. When there is deception by commission, there is an intentional level of control of both the quantity and quality of information the relational partner receives. This type of deception includes:
- Lies of convenience (commonly referred to as white lies) : This is when information is presented as slightly false and there may be minimal consequence to presenting the information as such. Oftentimes these white lies are communicated to enable one to feel less guilty or to ensure that someone’s feelings are not hurt. When one of the authors of this chapter was pregnant, they asked their husband if they looked OK in an outfit. Sometimes he said "yes." Once, when they were wearing an orange maternity dress, he said "You look like a pumpkin" and the author immediately started to cry. Would it have been better for him, in that case, to tell a white lie and just say “yes”? What purpose do white lies serve? They usually function as social lubrication—for purposes of smoothing over a relationship and keeping a relationship friction-free.
- Lies of exaggeration : An exaggeration is a type of deception by commission that includes the embellishing of facts or the stretching of the truth (which can get more elaborate over time). When someone exaggerates or overstates by playing with the boundaries of what is considered factual or truthful, this type of misrepresentation can lead to mistrust in a relationship given the blurring of boundaries between truth and fiction.
- Bald-faced lies : A bald-faced lie is a type of deception that involves an outright falsification of information. When you communicate a bald-faced lie, there exists an intent to truly deceive someone. With a bald-faced lie, there is going to be a greater emotional impact or consequence to the relationship if the lie is discovered as the risk of destroying trust in a relationship is greater.
Why Do We Deceive?
If we know that deception in a relationship carries with it the risk of destroying the trust we have built in our relationships, why would we decide to deceive someone in the first place? There are many reasons we might contemplate or use to determine and justify why it is OK to engage in any act of deception.
- Altruistic, or to protect and avoid hurting someone (their resources, self-image, or safety)
- Self-serving and for personal gain; to avoid undesirable consequences (negative consequences)
- To gain resources such as time, money, affection, and status
- To avoid harm or loss of resources
- To protect one’s self-image and save face
- For entertainment
Reflect on your past relationships and times you have engaged in any level of deception or felt you were deceived, and consider why. Do these reasons seem reasonable to you? We may find we can justify reasons (big or small) on why we might need to deceive in a relationship, but we also have to consider the short-term and long-term effects on a relationship if deception becomes commonplace.
Every communication act has a consequence, and we should be prepared to accept these consequences should we choose to engage in any form of deception in our relationships. First and foremost, as indicated earlier, if our relational partners find out we have withheld any information and they perceive us to be lying, there will necessarily be some kind of harm to the relationship and/or a loss of trust. We should expect the relational partner to be more guarded on whether to completely trust us in future interactions. There may also be collateral damage or harm to others who aren’t directly involved simply because they are in your orbit and may peripherally experience an after effect of the deception. Finally, deception can bring on other relational consequences such as punishment, damage to your reputation, or even a lingering guilty conscience that can get in the way of future carefree and open conversations.
Given these reasons/effects, do you advocate that deception or lying is necessary to some extent in a relationship?
The novel Big Little Lies by Liane Moriarty (and the subsequent mini-series that stemmed from it) depicts five main characters who are each faced with keeping secrets. These secrets vary in their depth and degree and the characters are seen grappling with how to best navigate keeping these secrets and to who they deceive versus disclose the truth too. Each of the women has different motivations for why they choose to deceive and each ends up having to deal with the different impacts and affects their deception has on their relationships with each other and others around them.
Gaslighting
Common Forms of Gaslighting
- blaming the other person for the problem
- minimizing the seriousness of the event
- diminishing the other person’s self-concept
- ridiculing the other person
- verbal attacks
- changing the subject
- blatant lying
- denial that something occurred
How to Respond to Gaslighting with Communication Competence
It is important to recognize that over time gaslighting can have damaging effects on an individual's self-concept, mental health, and overall well-being. If you find yourself using the gaslighting techniques described earlier, work on breaking the cycle by developing your assertiveness, emotional intelligence, and conflict management strategies to better address problems as they arise. If you believe that someone in your life is gaslighting you, it is worthwhile to develop a communication response strategy:


2.28: Outcome- Communicating the Value Proposition
What you’ll be able to do: define and communicate an organization’s value proposition in a competitive marketplace
Once you know your target market, you must have a compelling way to communicate your value proposition. This requires the marketer to answer a number of questions:
- What is value? Each customer will weigh the benefits and the costs of an offering differently and determine whether it is providing value. It is important to understand how customers perceive value.
- What is the value this offering provides to the target customer? You hope that you have selected target customers that view the value that you provide favorably, but the marketer has to test and refine the assumption that the offering is actually providing value to the target customer.
- How is the value provided different from the value that competitors provide? Each time a competitor shifts its offering(s), that change will have an impact on the perceived value of your offering. In a competitive marketplace, it becomes important to understand and react to changes, but also to identify the value that you provide that is most difficult for others to copy.
- How are you communicating the promise of value to target customers? With so many marketing channels and messages all around, customers have a very short attention span. The marketer has to grab that attention and communicate value to customers in only a few seconds.
Learning Activities
The learning activities for this section include the following:
- Reading: Value for the Customer
- Reading: Communicating the Value Proposition
- Self Check: Communicating the Value Proposition
Contributors and Attributions
CC licensed content, Original
- Outcome: Communicating the Value Proposition. Provided by : Lumen Learning. License : CC BY: Attribution


6.7: Inverse Trigonometric Functions
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In previous sections, we have evaluated the trigonometric functions at various angles, but at times we need to know what angle would yield a specific sine, cosine, or tangent value. For this, we need inverse functions. Recall that for a one-to-one function, if \(f(a)=b\), then an inverse function would satisfy \(f^{-1} (b)=a\).
You probably are already recognizing an issue – that the sine, cosine, and tangent functions are not one-to-one functions. To define an inverse of these functions, we will need to restrict the domain of these functions to yield a new function that is one-to-one. We choose a domain for each function that includes the angle zero.
On these restricted domains, we can define the inverse sine, inverse cosine, and inverse tangent functions.
INVERSE SINE, COSINE, AND TANGENT FUNCTIONS and their inverses
For angles in the interval \(\left[-\dfrac{\pi }{2} ,\dfrac{\pi }{2} \right]\), if \(\sin \left(\theta \right)=a\), then \(\sin ^{-1} \left(a\right)=\theta\)
\(\sin ^{-1} \left(x\right)\) has domain [-1, 1] and range \(\left[-\dfrac{\pi }{2} ,\dfrac{\pi }{2} \right]\)
The \(\sin ^{-1} \left(x\right)\) is sometimes called the arcsine function, and notated \(\arcsin \left(a\right)\).
For angles in the interval \(\left[0,\pi \right]\), if \(\cos \left(\theta \right)=a\), then \(\cos ^{-1} \left(a\right)=\theta\)
\(\cos ^{-1} \left(x\right)\) has domain [-1, 1] and range \(\left[0,\pi \right]\)
The \(\cos ^{-1} \left(x\right)\) is sometimes called the arccosine function, and notated \(\arccos \left(a\right)\).
For angles in the interval \(\left(-\dfrac{\pi }{2} ,\dfrac{\pi }{2} \right)\), if \(\tan \left(\theta \right)=a\), then \(\tan ^{-1} \left(a\right)=\theta\)
\(\tan ^{-1} \left(x\right)\) has domain of all real numbers and range \(\left(-\dfrac{\pi }{2} ,\dfrac{\pi }{2} \right)\)
The \(\tan ^{-1} \left(x\right)\) is sometimes called the arctangent function, and notated \(\arctan \left(a\right)\).
The graphs of the inverse functions are shown here:
Notice that the output of each of these inverse functions is an \(angle\).
Example \(\PageIndex{1}\)
Evaluate
- \(\sin ^{-1} \left(\dfrac{1}{2} \right)\)
- \(\sin ^{-1} \left(-\dfrac{\sqrt{2} }{2} \right)\)
- \(\cos ^{-1} \left(-\dfrac{\sqrt{3} }{2} \right)\)
- \(\tan ^{-1} \left(1\right)\)
Solution
a) Evaluating \(\sin ^{-1} \left(\dfrac{1}{2} \right)\) is the same as asking what angle would have a sine value of \(\dfrac{1}{2}\). In other words, what angle \(\theta\) would satisfy \(\sin \left(\theta \right)=\dfrac{1}{2}\)?
There are multiple angles that would satisfy this relationship, such as \(\dfrac{\pi }{6}\) and \(\dfrac{5\pi }{6}\), but we know we need the angle in the range of \(\sin ^{-1} \left(x\right)\), the interval \(\left[-\dfrac{\pi }{2} ,\dfrac{\pi }{2} \right]\), so the answer will be \[\sin ^{-1} \left(\dfrac{1}{2} \right)=\dfrac{\pi }{6}\nonumber\]
Remember that the inverse is a function so for each input, we will get exactly one output.
b) Evaluating \(\sin ^{-1} \left(-\dfrac{\sqrt{2} }{2} \right)\), we know that \(\dfrac{5\pi }{4}\) and \(\dfrac{7\pi }{4}\) both have a sine value of \(-\dfrac{\sqrt{2} }{2}\), but neither is in the interval \(\left[-\dfrac{\pi }{2} ,\dfrac{\pi }{2} \right]\). For that, we need the negative angle coterminal with \(\dfrac{7\pi }{4}\). \[\sin ^{-1} \left(-\dfrac{\sqrt{2} }{2} \right)=-\dfrac{\pi }{4}\nonumber\]
c) Evaluating \(\cos ^{-1} \left(-\dfrac{\sqrt{3} }{2} \right)\), we are looking for an angle in the interval \(\left[0,\pi \right]\) with a cosine value of \(-\dfrac{\sqrt{3} }{2}\). The angle that satisfies this is \[\cos ^{-1} \left(-\dfrac{\sqrt{3} }{2} \right)=\dfrac{5\pi }{6}\nonumber\]
d) Evaluating \(\tan ^{-1} \left(1\right)\), we are looking for an angle in the interval \(\left(-\dfrac{\pi }{2} ,\dfrac{\pi }{2} \right)\) with a tangent value of 1. The correct angle is \[\tan ^{-1} \left(1\right)=\dfrac{\pi }{4}\nonumber\]
Exercise \(\PageIndex{1}\)
Evaluate
- \(\sin ^{-1} \left(-1\right)\)
- \(\tan ^{-1} \left(-1\right)\)
- \(\cos ^{-1} \left(-1\right)\)
- \(\cos ^{-1} \left(\dfrac{1}{2} \right)\)
- Answer
-
a) \(-\dfrac{\pi }{2}\)
b) \(-\dfrac{\pi }{4}\)
c) \(\pi\)
d) \(\dfrac{\pi }{3}\)
Example \(\PageIndex{2}\)
Evaluate \(\sin ^{-1} \left(0.97\right)\) using your calculator.
Solution
Since the output of the inverse function is an angle, your calculator will give you a degree value if in degree mode, and a radian value if in radian mode.
In radian mode, \[\sin ^{-1} (0.97) \approx 1.3252\nonumber\]
In degree mode, \[\sin ^{-1} \left(0.97\right)\approx 75.93{}^\circ\nonumber\]
Exercise
Evaluate \(\cos ^{-1} \left(-0.4\right)\) using your calculator.
- Answer
-
\[1.9823\text{ or }113.578\mathrm{{}^\circ}\nonumber\]
In Section 5.5, we worked with trigonometry on a right triangle to solve for the sides of a triangle given one side and an additional angle. Using the inverse trig functions, we can solve for the angles of a right triangle given two sides.
Example \(\PageIndex{3}\)
Solve the triangle for the angle \(\theta\).
Solution
Since we know the hypotenuse and the side adjacent to the angle, it makes sense for us to use the cosine function.
\[\cos \left(\theta \right)=\dfrac{9}{12}\nonumber\]Using the definition of the inverse,
\[\theta =\cos ^{-1} \left(\dfrac{9}{12} \right)\nonumber\]Evaluating
\[\theta \approx 0.7227\text{, or about }41.4096\mathrm{{}^\circ}\nonumber\]
There are times when we need to compose a trigonometric function with an inverse trigonometric function. In these cases, we can find exact values for the resulting expressions
Example \(\PageIndex{4}\)
Evaluate \(\sin ^{-1} \left(\cos \left(\dfrac{13\pi }{6} \right)\right)\).
Solution
a) Here, we can directly evaluate the inside of the composition.
\[\cos \left(\dfrac{13\pi }{6} \right)=\dfrac{\sqrt{3} }{2}\nonumber\]
Now, we can evaluate the inverse function as we did earlier.
\[\sin ^{-1} \left(\dfrac{\sqrt{3} }{2} \right)=\dfrac{\pi }{3}\nonumber\]
Exercise \(\PageIndex{3}\)
Evaluate \(\cos ^{-1} \left(\sin \left(-\dfrac{11\pi }{4} \right)\right)\).
- Answer
-
\[\sin \left(-\dfrac{11\pi }{4} \right)=-\dfrac{\sqrt{2} }{2} . \cos ^{-1} \left(-\dfrac{\sqrt{2} }{2} \right)=\dfrac{3\pi }{4} \nonumber\]
Example \(\PageIndex{5}\)
Find an exact value for \(\sin \left(\cos ^{-1} \left(\dfrac{4}{5} \right)\right)\).
Solution
Beginning with the inside, we can say there is some angle so \(\theta =\cos ^{-1} \left(\dfrac{4}{5} \right)\), which means \(\cos \left(\theta \right)=\dfrac{4}{5}\), and we are looking for \(\sin \left(\theta \right)\). We can use the Pythagorean identity to do this.
\[\sin ^{2} \left(\theta \right)+\cos ^{2} \left(\theta \right)=1\nonumber\]Using our known value for cosine
\[\sin ^{2} \left(\theta \right)+\left(\dfrac{4}{5} \right)^{2} =1\nonumber\]Solving for sine
\[\sin ^{2} \left(\theta \right)=1-\dfrac{16}{25}\nonumber\]
\[\sin \left(\theta \right)=\pm \sqrt{\dfrac{9}{25} } =\pm \dfrac{3}{5}\nonumber\]
Since we know that the inverse cosine always gives an angle on the interval \(\left[0,\pi \right]\), we know that the sine of that angle must be positive, so \[\sin \left(\cos ^{-1} \left(\dfrac{4}{5} \right)\right)=\sin (\theta )=\dfrac{3}{5}\nonumber\]
Example \(\PageIndex{6}\)
Find an exact value for \(\sin \left(\tan ^{-1} \left(\dfrac{7}{4} \right)\right)\).
Solution
While we could use a similar te chnique as in the last example, we will demonstrate a different technique here. From the inside, we know there is an angle so \(\tan \left(\theta \right)=\dfrac{7}{4}\). We can envision this as the opposite and adjacent sides on a right triangle.
Using the Pythagorean Theorem, we can find the hypotenuse of this triangle:
\[4^{2} +7^{2} =hypotenuse ^{2}\nonumber\]
\[hypotenuse=\sqrt{65}\nonumber\]
Now, we can represent the sine of the angle as opposite side divided by hypotenuse.
\[\sin \left(\theta \right)=\dfrac{7}{\sqrt{65} }\nonumber\]
This gives us our desired composition
\[\sin \left(\tan ^{-1} \left(\dfrac{7}{4} \right)\right)=\sin (\theta )=\dfrac{7}{\sqrt{65} } .\nonumber\]
Exercise \(\PageIndex{4}\)
Evaluate \(\cos \left(\sin ^{-1} \left(\dfrac{7}{9} \right)\right)\).
- Answer
-
Let \(\theta =\sin ^{-1} \left(\dfrac{7}{9} \right)\) so \[\sin (\theta )=\dfrac{7}{9}\nonumber\]
Using Pythagorean Identity, \(\sin ^{2} \theta +\cos ^{2} \theta =1\), so \[\left(\dfrac{7}{9} \right)^{2} +\cos ^{2} \theta =1\nonumber\]
Solving, \[\cos \left(\sin ^{-1} \left(\dfrac{7}{9} \right)\right)=\cos \left(\theta \right)=\dfrac{4\sqrt{2} }{9}\nonumber\]
We can also find compositions involving algebraic expressions
Example \(\PageIndex{7}\)
Find a simplified expression for \(\cos \left(\sin ^{-1} \left(\dfrac{x}{3} \right)\right)\), for \(-3\le x\le 3\).
Solution
We know there is an angle \(\theta\) so that \(\sin \left(\theta \right)=\dfrac{x}{3}\). Using the Pythagorean Theorem,
\[\sin ^{2} \left(\theta \right)+\cos ^{2} \left(\theta \right)=1\nonumber\]Using our known expression for sine
\[\left(\dfrac{x}{3} \right)^{2} +\cos ^{2} \left(\theta \right)=1\nonumber\]Solving for cosine
\[\cos ^{2} \left(\theta \right)=1-\dfrac{x^{2} }{9}\nonumber\]
\[\cos \left(\theta \right)=\pm \sqrt{\dfrac{9-x^{2} }{9} } =\pm \dfrac{\sqrt{9-x^{2} } }{3}\nonumber\]
Since we know that the inverse sine must give an angle on the interval \(\left[-\dfrac{\pi }{2} ,\dfrac{\pi }{2} \right]\), we can deduce that the cosine of that angle must be positive. This gives us
\[\cos \left(\sin ^{-1} \left(\dfrac{x}{3} \right)\right)=\dfrac{\sqrt{9-x^{2} } }{3}\nonumber\]
Exercise \(\PageIndex{5}\)
Find a simplified expression for \(\sin \left(\tan ^{-1} \left(4x\right)\right)\), for \(-\dfrac{1}{4} \le x\le \dfrac{1}{4}\).
- Answer
-
Let \(\theta =\tan ^{-1} \left(4x\right)\), so \(\tan (\theta )=4x\). We can represent this on a triangle as \(\tan (\theta )=\dfrac{4x}{1}\).
The hypotenuse of the triangle would be \(\sqrt{\left(4x\right)^{2} +1}\). \[\sin \left(\tan ^{-1} \left(4x\right)\right)=\sin (\theta )=\dfrac{4x}{\sqrt{16x^{2} +1} }\nonumber\]
Important Topics of This Section
- Inverse trig functions: arcsine, arccosine and arctangent
- Domain restrictions
- Evaluating inverses using unit circle values and the calculator
- Simplifying numerical expressions involving the inverse trig functions
- Simplifying algebraic expressions involving the inverse trig functions


6.1: Problem Solving to Find Entrepreneurial Solutions
By the end of this section, you will be able to:
- Define problem solving in the context of entrepreneurship
- Describe and compare the adaptive model and the innovative model of problem solving
- Identify the skills entrepreneurs need for effective problem solving
- Identify types of problem solvers
As you’ve learned, entrepreneurs often visualize an opportunity gap, a gap between what exists and what could exist, as Hirabayashi and Lidey did with Shine. Entrepreneurial problem solving is the process of using innovation and creative solutions to close that gap by resolving societal, business, or technological problems. Sometimes, personal problems can lead to entrepreneurial opportunities if validated in the market. The entrepreneur visualizes the prospect of filling the gap with an innovative solution that might entail the revision of a product or the creation of an entirely new product. In any case, the entrepreneur approaches the problem-solving process in various ways. This chapter is more about problem solving as it pertains to the entrepreneur’s thought process and approach rather than on problem solving in the sense of opportunity recognition and filling those gaps with new products.
For example, as we read in Identifying Entrepreneurial Opportunity , Sara Blakely (as shown in Figure 6.2 ) saw a need for body contouring and smoothing undergarments one day in the late 1990s when she was getting dressed for a party and couldn’t find what she needed to give her a silhouette she’d be pleased with in a pair of slacks. She saw a problem: a market need. But her problem-solving efforts are what drove her to turn her solution (Spanx undergarments) into a viable product. Those efforts came from her self-admitted can-do attitude: “It’s really important to be resourceful and scrappy—a glass half-full mindset.” 1 Her efforts at creating a new undergarment met resistance with hosiery executives, most of whom were male and out of touch with their female consumers. The hosiery owner who decided to help Blakely initially passed on the idea until running it by his daughters and realizing she was on to something. That something became Spanx, and today, Blakely is a successful entrepreneur. 2
Before getting into the heart of this chapter, we need to make a distinction: Decision making is different from problem solving . A decision is needed to continue or smooth a process affecting the operation of a firm. It can be intuitive or might require research and a long period of consideration. Problem solving, however, is more direct. It entails the solution of some problem where a gap exists between a current state and a desired state. Entrepreneurs are problem solvers who offer solutions using creativity or innovative ventures that exploit opportunities. This chapter focuses on different approaches to problem solving and need recognition that help potential entrepreneurs come up with ideas and refine those ideas.
Two Problem Solving Models: Adaptive and Innovative
There are two prominent established problem-solving models: adaptive and innovative . A renowned British psychologist, Michael Kirton, developed the Kirton Adaption-Innovation (KAI) Inventory to measure an individual’s style of problem solving. 3 Problem-solving preferences are dependent on the personality characteristics of originality, conformity, and efficiency, according to Kirton. The KAI inventory identifies an individual’s problem-solving approach by measuring agreement with statements that align with characteristics, such as the ability to produce many novel ideas, to follow rules and get along in groups, and to systematically orient daily behavior. The results categorize an individual as an innovator or an adaptor. Innovators are highly original, do not like to conform, and value efficiency less than adaptors.
The first and more conservative approach an entrepreneur may use to solve problems is the adaptive model. The adaptive model seeks solutions for problems in ways that are tested and known to be effective. An adaptive model accepts the problem definition and is concerned with resolving problems rather than finding them. This approach seeks greater efficiency while aiming at continuity and stability. The second and more creative approach is the innovative model of entrepreneurial problem solving, which uses techniques that are unknown to the market and that bring advantage to an organization. An innovative problem-solving style challenges the problem definition, discovers problems and avenues for their solutions, and questions existing assumptions—in a nutshell, it does things differently. It uses outside-the-box thinking and searches for novel solutions. Novelty is a shared trait of creative entrepreneurship, and it’s why entrepreneurs gravitate toward this method of problem solving. According to Dr. Shaun M. Powell, a senior lecturer at the University of Wollongong, Australia: “Creative entrepreneurs are notable for a distinctive management style that is based on intuition, informality and rapid decision making, whereas the more conventional thinking styles are not in accord with the unique attributes of creative entrepreneurs.” 4 This way of problem solving doesn’t alter an existing product. It is the creation of something entirely new.
For example, healthcare facilities have long been known as a source of methicillin-resistant Staphylococcus aureus (MRSA), a deadly infection that can have long-term effects on patients. Vital Vio, led by Colleen Costello, has developed white light technology that effectively disinfects healthcare facilities by targeting a molecule specific to bacteria.  An adaptive problem-solving model would seek to minimize harm of MRSA within a hospital—to respond to it—whereas the Vital Vio is an entirely new technique that seeks to eliminate it. Adaptive solutions to MRSA include established processes and protocols for prevention, such as having doctors, nurses, and other healthcare providers clean their hands with soap and water, or an alcohol-based hand rub before and after patient care, testing patients to see if they have MRSA on their skin, cleaning hospital rooms and medical equipment, and washing and drying clothes and bed linens in the warmest recommended temperatures. 5
Visit Inc. Magazine for support and advice for up-and-coming startups to learn more. Examples of how “Dorm Room” entrepreneurs spot and pursue opportunities are shared along with tips and advice for making your startup a success.
Problem-Solving Skills
While identifying problems is a necessary part of the origin of the entrepreneurial process, managing problems is an entirely different aspect once a venture is off the ground and running. An entrepreneur does not have the luxury of avoiding problems and is often responsible for all problem solving in a startup or other form of business. There are certain skills that entrepreneurs possess that make them particularly good problem solvers. Let’s examine each skill (shown in Figure 6.3 ) .
Critical Thinking
Critical thinking is the complex analysis of a problem or issue with the goal of solving the problem or making a decision. The entrepreneur analyzes and peels away the layers of a problem to find the core of an issue facing a business. The entrepreneur focuses on the heart of the problem and responds reasonably and openly to suggestions for solving it. Critical thinking is not only important for developing entrepreneurial ideas: it is a sought-after asset in education and employment. Entrepreneur Rebecca Kantar dropped out of Harvard in 2015 to found the tech startup Imbellus, which aims to replace standardized college admissions tests like the SAT with interactive scenarios that test critical-thinking skills. Many standardized tests may include multiple choice questions asking for the answer to a straightforward knowledge question or math problem. Kantar seeks to create tests that are more concerned with the analytic ability and reasoning that goes into the process of solving the problem. Imbellus says it aims to test “how people think,” not just what they know. The platform, which has not yet launched, will use simulations for its user assessments. 6
Communication
Communication skills , the ability to communicate messages effectively to an intended recipient, are the skills entrepreneurs use to pool resources for the purposes of investigating solutions leading to innovative problem solving and competitive advantage. Good communication allows for the free association of ideas between entrepreneurs and businesses. It can illustrate a problem area or a shared vision, and seeks stakeholder buy-in from various constituencies. Networking and communication within an industry allow the entrepreneur to recognize the position of an enterprise in the market and work toward verbalizing solutions that move an organization beyond its current state. By “verbalizing,” we mean communication from and with the company/entity. Internal communications include company emails, newsletters, presentations, and reports that can set strategic goals and objectives, and report on what has been accomplished and what goals and objectives remain, so that employees within an organization are knowledgeable and can work on solving problems that remain within the organization. External communications could include press releases, blogs and websites, social media, public speeches, and presentations that explain the company’s solutions to problems. They could also be investor pitches complete with business plans and financial projections.
Ideation exercises, such as brainstorming sessions (discussed in Creativity, Innovation, and Invention , are good communication tools that entrepreneurs can use to generate solutions to problems. Another such tool is a hackathon —an event, usually hosted by a tech company or organization, which brings together programmers and workers with other degrees of specialization within the company, community, or organization to collaborate on a project over a short period of time. These can last from twenty-four hours to a few days over a weekend. A hackathon can be an internal company-wide initiative or an external event that brings community participants together. A business model canvas, which is covered in Business Model and Plan and other activities outlined in other chapters can be used internally or externally to identify problems and work toward creating a viable solution.
Networking is an important manifestation of useful communication. What better method is there of presenting one’s concept, gaining funding and buy-in, and marketing for the startup than through building a network of individuals willing to support your venture? A network may consist of potential employees, customers, board members, outside advisors, investors, or champions (people who just love your product) with no direct vested interest. Social networks consist of weak ties and strong ties. Sociologist Mark Granovetter studied such networks back in the 1970s, and his findings still apply today, even if we include social media networks in the definition too. Weak ties facilitate flow of information and community organization, he said, whereas strong ties represent strong connections among close friends, family members, and supportive coworkers. 7 Strong ties require more work to maintain than weak ties (as illustrated by the strong lines and weak dotted lines in Figure 6.4 ) and in a business context, they don’t lead to many new opportunities. Weak ties, in contrast, do open doors in that they act as bridges to other weak ties within functional areas or departments that you might not have had access to directly or through strong ties. 8
In fact, many young entrepreneurs, including tech entrepreneur Oliver Isaacs, realize college is a great place to begin building teams. Isaacs is the founder of viral opinion network Amirite.com, which is widely credited as the place where Internet memes started and online slang got a foothold. 9 Amirite.com consists of a large network of pages and partnerships on Facebook and Instagram that reach 15 million users each month. Isaacs recommends using your alumni network to build a team and customer base for your own venture because you never know if you’re talking to a future employee or partner.
Sharing of ideas and resources is highly valued in the entrepreneurial process. Communication is a vital skill in problem solving because the ability to identify and articulate the problem (define the problem space) is necessary to adequately address a problem. A problem can be too vague or broad or narrow. Thus, communicating the problem is important, as is conveying the solution.
Decisiveness
Decisiveness is as it sounds: the ability to make a quick, effective decision, not letting too much time go by in the process. Entrepreneurs must be productive, even in the face of risk. They often rely on intuition as well as on hard facts in making a choice. They ask what problem needs to be solved, think about solutions, and then consider the means necessary to implement an idea. And the decisions must be informed with research.
For example, as explained in Adam Grant’s book The Originals , the co-founders of Warby Parker, a venture-backed startup focused on the eyewear industry, started their company while they were graduate students. At the time they knew little about the industry, but after conducting some detailed research, they learned that the industry was dominated by one major player—Luxottica. They used this information and other data to refine their strategy and business model (focusing mainly on value, quality, and convenience via an online channel). By the time they decided to launch the business, they had thought through the key details, and they attained rapid early success. Today Warby Parker has over 100 retail stores in the US, is profitable, and is valued at almost $2 billion.
Decisiveness is the catapult to progress. Amazon founder Jeff Bezos preaches the importance of decisiveness throughout his organization. Bezos believes that decisiveness can even lead to innovation. Bezos advocates for making decisions after obtaining 70 percent of the information you need to do so: “Being wrong may be less costly than you think, whereas being slow is going to be expensive for sure,” Bezos wrote in a 2017 annual letter to stockholders. 10
Ability to Analyze Data
Data analysis is the process of analyzing data and modeling it into a structure that leads to innovative conclusions. Identifying Entrepreneurial Opportunity covered much of the sources of data that entrepreneurs might seek. But it is one thing to amass information and statistics. It is another to make sense of that data, to use it to fill a market need or forecast a trend to come. Successful founders know how to pose questions about and make meaning out of information. And if they can’t do that themselves, they know how to bring in experts who can.
In addition to public sources of broad data, a business can collect data on customers when they interact with the company on social media or when they visit the company website, especially if they complete a credit card transaction. They can collect their own specific data on their own customers, including location, name, activity, and how they got to the website. Analyzing these data will give the entrepreneur a better idea about the interested audience’s demographic.
In entrepreneurship, analyzing data can help with opportunity recognition, creation, and assessment by analyzing data in a variety of ways. Entrepreneurs can explore and leverage different data sources to identify and compare “attractive” opportunities, since such analyses can describe what has happened, why it happened, and how likely it is to happen again in the future. In business in general, analytics is used to help managers/entrepreneurs gain improved insight about their business operations/emerging ventures and make better, fact-based decisions.
Analytics can be descriptive, predictive, or prescriptive. Descriptive analytics involves understanding what has happened and what is happening; predictive analytics uses data from past performance to estimate future performance; and prescriptive analytics uses the results of descriptive and predictive analytics to make decisions. Data analysis can be applied to manage customer relations, inform financial and marketing activities, make pricing decisions, manage the supply chain, and plan for human resource needs, among other functions of a venture. In addition to statistical analysis, quantitative methods, and computer models to aid decision-making, companies are also increasingly using artificial intelligence algorithms to analyze data and make quick decisions.
Understanding of Business and Industry
Entrepreneurs need sound understanding of markets and industries. Often times, they are already working in a large organization when they see growth opportunities or inefficiencies in a market. The employee gains a deep understanding of the industry at hand. If the employee considers a possible solution for a problem, this solution might become the basis for a new business.
For example, consider a marketing agency that used traditional marketing for thirty years. This agency had an established clientele. An executive in the organization began studying social media analytics and social media. The executive approached the owner of the business to change processes and begin serving clients through social media, but the owner refused. Clients within the agency began to clamor for exposure on social media. The marketing executive investigated the possibility of building an agency in her locale servicing clients who wish to utilize social media. The marketing executive left the organization and started her own agency (providing, of course, that this is in compliance with any noncompete clauses in her contract). Her competitive advantage was familiarity with both traditional and social media venues. Later, the original agency started floundering because it did not offer social media advertising. Our intrepid executive purchased the agency to gain the clientele and serve those wishing to move away from traditional marketing.
A similar experience occurred for entrepreneur Katie Witkin. After working in traditional marketing roles, the University of Wisconsin-Madison graduate, pictured in Figure 6.5 , left agency life behind four years out of college to cofound her own company, AGW Group. In 2009, Witkin had been interning at a music marketing agency that didn’t have a social media department. She knew, both from her time at college and from observing industry trends, that social media was changing the way companies connected with customers. For her own venture, she expanded the focus to all supporting brands to manage all things digital. Today, the cultural and marketing communications agency has fifteen employees and big-name clients ranging from HBO to Red Bull. 11
Resourcefulness
Resourcefulness
is the ability to discover clever solutions to obstacles. Sherrie Campbell, a psychologist, author, and frequent contributor to
Entrepreneur
magazine on business topics, put it this way:
“There is not a more useful or important trait to possess than resourcefulness in the pursuit of success. Resourcefulness is a mindset, and is especially relevant when the goals you have set are difficult to achieve or you cannot envision a clear path to get to where you desire to go. With a resourcefulness mindset you are driven to find a way. An attitude of resourcefulness inspires out-of-the-box thinking, the generation of new ideas, and the ability to visualize all the possible ways to achieve what you desire. Resourcefulness turns you into a scrappy, inventive and enterprising entrepreneur. It places you a cut above the rest.”
12
Entrepreneurs start thinking about a business venture or startup by talking to people and procuring experts to help create, fund, and begin a business. Entrepreneurs are risk takers, passionate about new endeavors. If they don’t have a college degree or a great deal of business experience, they understand there are many resources available to support them in the endeavor, such as the Service Corps of Retired Executives (SCORE) and the Small Business Administration (SBA). There are many sources available to fund the business with little or no debt and options, as you will see in the chapter on Entrepreneurial Finance and Accounting . The entrepreneur follows a vision and researches opportunities to move toward a dream.
For example, in the late 1990s, Bill McBean and his business partner Billy Sterett had an opportunity to buy an underperforming auto dealership that would make their company the dominant one in the market. Neither wanting to take cash from other ventures nor wanting to borrow more money and tie themselves to more debt, the entrepreneurs were resourceful by finding another path forward to obtaining the money necessary for the acquisition they both coveted. They changed banks and renegotiated their banking payback requirements, lowering their interest payments, reducing fees, and lowering their monthly payments, ultimately freeing up a significant amount of cash that allowed them to buy the new company. 13
Types of Problem Solvers
Entrepreneurs have an insatiable appetite for problem solving. This drive motivates them to find a resolution when a gap in a product or service occurs. They recognize opportunities and take advantage of them. There are several types of entrepreneurial problem solvers, including self-regulators, theorists, and petitioners.
Self-Regulating Problem Solvers
Self-regulating problem solvers are autonomous and work on their own without external influence. They have the ability to see a problem, visualize a possible solution to the problem, and seek to devise a solution, as Figure 6.6 illustrates. The solution may be a risk, but a self-regulating problem solver will recognize, evaluate, and mitigate the risk. For example, an entrepreneur has programmed a computerized process for a client, but in testing it, finds the program continually falls into a loop, meaning it gets stuck in a cycle and doesn’t progress. Rather than wait for the client to find the problem, the entrepreneur searches the code for the error causing the loop, immediately edits it, and delivers the corrected program to the customer. There is immediate analysis, immediate correction, and immediate implementation. The self-regulating problem solvers’ biggest competitive advantage is the speed with which they recognize and provide solutions to problems.
Theorist Problem Solvers
Theorist problem solvers see a problem and begin to consider a path toward solving the problem using a theory. Theorist problem solvers are process oriented and systematic. While managers may start with a problem and focus on an outcome with little consideration of a means to an end, entrepreneurs may see a problem and begin to build a path with what is known, a theory, toward an outcome. That is, the entrepreneur proceeds through the steps to solve the problem and then builds on the successes, rejects the failures, and works toward the outcome by experimenting and building on known results. At this point, the problem solver may not know the outcome, but a solution will arise as experiments toward a solution occur. Figure 6.7 shows this process.
For example, if we consider Marie Curie as an entrepreneur, Curie worked toward the isolation of an element. As different approaches to isolating the element failed, Curie recorded the failures and attempted other possible solutions. Curie’s failed theories eventually revealed the outcome for the isolation of radium. Like Curie, theorists use considered analysis, considered corrective action, and a considered implementation process. When time is of the essence, entrepreneurs should understand continual experimentation slows the problem-solving process.
Petitioner Problem Solvers
Petitioner problem solvers ( Figure 6.8 ) see a problem and ask others for solution ideas. This entrepreneur likes to consult a person who has “been there and done that.” The petitioner might also prefer to solve the problem in a team environment. Petitioning the entrepreneurial team for input ensures that the entrepreneur is on a consensus-driven path. This type of problem solving takes the longest to complete because the entrepreneur must engage in a democratic process that allows all members on the team to have input. The process involves exploration of alternatives for the ultimate solution. In organizational decision-making, for example, comprehensiveness is a measure of the extent a firm attempts to be inclusive or exhaustive in its decision-making. Comprehensiveness can be gauged by the number of scheduled meetings, the process by which information is sought, the process by which input is obtained from external sources, the number of employees involved, the use of specialized consultants and the functional expertise of the people involved, the years of historical data review, and the assignment of primary responsibility, among other factors. Comprehensive decision-making would be an example of a petitioner problem-solving style, as it seeks input from a vast number of team members.
A charette —a meeting to resolve conflicts and identify solutions—is another example that employs a petitioner problem-solving approach. Often times, a developer of a new project might hold a community charette to aid in the design of a project, hoping to gain approval from elected officials. In the building example, this could consist of the developer and his team of architects, project designers, and people with expertise in the project working alongside community members, business executives, elected officials, or representatives like staff members or citizen-appointed boards like a planning board. Such an activity is representative of a petitioner problem-solving approach, as opposed to a developer representative designing the project with no input from anyone else.
In summary, there is no right or wrong style of problem solving; each problem solver must rely on the instincts that best drive innovation. Further, they must remember that not all problem-solving methods work in every situation. They must be willing to adapt their own preference to the situation to maximize efficiency and ensure they find an effective solution. Attempting to force a problem-solving style may prevent an organization from finding the best solution. While general entrepreneurial problem-solving skills such as critical thinking, decisiveness, communication, and the ability to analyze data will likely be used on a regular basis in your life and entrepreneurial journey, other problem-solving skills and the approach you take will depend on the problem as it arises.
There are a number of resources online that can help analyze your problem-solving abilities. Mindtools.com is one such resource. These are useful to learn your general problem-solving tendencies before being called upon to apply them in a real-world setting. One of the problem-solving techniques available from mindtools.com offers that problems can be addressed from six different perspectives. Called CATWOE, the approach is an acronym for Customers, Actors (people within the organization), Transformative, Worldwide, Owner, and Environment (organizational).


5.1: Demographic Factors
By the end of this section, you should be able to:
- Define demographics.
- Describe the fastest-growing demographics in the United States.
- Discuss characteristics of underrepresented populations.
- Examine how projected population changes challenge public health policies and the implications for health care services.
Demographics are statistical data regarding the characteristics of the people living in a particular place, describing them based on categories such as age, race , ethnicity , sexual orientation , gender identity , ability, education level, income level, and marital status. Individuals belong to many demographic groups. For example, a person may belong to one group based on age, another based on race, and a third based on geographic location. This section examines demographics, focusing on rapidly growing underrepresented populations and on how the growth of these populations affects both public health policies and the provision of health care services.
Fastest-Growing Demographics
U.S. Census Bureau forecasts indicate that the United States will continue to experience significant demographic shifts in the next 40 years. By 2060, the U.S. population is expected to increase by 79 million people (U.S. Census Bureau, 2020), and changing demographics will have major implications for the national health care system. Community health and public health nurses must prepare to serve these changed populations. A more diverse nursing workforce will lead to better health outcomes for populations (American Association of Colleges of Nursing, 2023). This section reviews the most rapidly expanding population groups within the United States.
Baby Boomers
One way to categorize populations is by generation, a period spanning about 20 to 30 years that includes everyone who is born and lives their lives at approximately the same time, experiencing similar social and cultural events. Until recently, baby boomers , or the generation born from 1946 to 1964, made up the largest generation in the United States—76 million births—and 71.6 million living adults in 2019 (Fry, 2020). As this large demographic group ages, the number of individuals over the age of 65 continues to increase. For example, although older adults represented 8 percent of the total population in 1950, they made up 16 percent of the population in 2020 and are projected to represent nearly 25 percent of the total population in 2060 (see Figure 5.2) (Centers for Disease Control and Prevention [CDC], 2022d).
The U.S. Census Bureau estimates that by 2030 all individuals in the United States categorized as baby boomers will be over 65 years old, marking a significant shift toward an older average age in the U.S. population (America Counts Staff, 2019). The growth of the baby boomer population is significant for nurses and other health care professionals because older adults tend to have a higher prevalence of health issues and chronic diseases, such as Alzheimer’s disease, diabetes, hypertension, and arthritis, that are related to aging (CDC, 2022d). As the proportion of older adults in the population increases, the incidence of age-related health conditions and deaths will also increase. Consequently, the need for health care services in nursing homes , long-term care , and home health care facilities in the United States will grow.
Racial and Ethnic Minorities
Another projected demographic change in the U.S. population is a shift in the numbers of racial and ethnic minorities in relation to the population as a whole. Ethnic minorities are population groups with a shared culture, tradition, religion, language, history, or other factors living in communities or areas where most people are from a different ethnic group. Between 2020 and 2060, the U.S. Census Bureau predicts major changes in the racial and ethnic diversity of the U.S. population. For example, the number of non-Hispanic White individuals is expected to decrease dramatically. In 2020, there were approximately 199 million non-Hispanic White individuals in the United States; that number is expected to fall to approximately 179 million by 2060, a 10 percent decrease. The decline in the non-Hispanic White demographic is related to a decrease in overall births and an increase in deaths over time.
During the same 40-year period, individuals who identify as two or more races are projected to be the fastest-growing racial or ethnic group in the United States. The U.S. Census Bureau estimates that Asian people will make up the second fastest-growing ethnic group, and Hispanic people will be the third fastest. The projected increase in the number of individuals who identify as Hispanic is attributed to an increase in the number of children born to parents who identify as Hispanic in the past decade, while the projected increase in net international migration is the primary driver for an increase in the number of individuals who identify as Asian. The U.S. Census Bureau also estimates that the population of individuals who are considered foreign-born will increase from 44 million in 2016 to approximately 69 million in 2060, making up 17 percent of the U.S. population (2020).
For nurses and other health care professionals, these rapidly changing demographics are significant because they have implications for the prevalence of disease and health disparities . The CDC defines health disparities as “preventable differences in the burden of disease, injury, violence, or opportunities to achieve optimal health that are experienced by socially disadvantaged populations” (CDC, 2020a, para. 1).
Heart disease, cancer, diabetes, and stroke are the most common causes of illness, disability, and death in the United States (CDC, 2022a). Underrepresented populations , such as ethnic minorities, tend to be impacted the most by chronic diseases —conditions like hypertension, diabetes, kidney disease, heart disease, and cancer—that individuals live with for a year or more that require ongoing medical attention, limit the activities of daily living, or both. Underrepresented populations are defined as subgroups within a population, often identified by race, ethnicity, age, sex, gender, sexual orientation, or socioeconomic status , whose representation in society is disproportionately low relative to their numbers (National Institutes of Health [NIH], 2023b). Chronic diseases affect certain racial and ethnic groups more than others:
- Between 2017 and 2018, diagnosed diabetes prevalence was higher among American Indians/Alaska Natives, people of Hispanic origin, and non-Hispanic Black people than among White people (CDC, 2020c).
- In 2018, Asian people comprised 6 percent of the U.S. population but accounted for approximately 2 percent of new HIV cases (CDC, 2020b).
- Asian/Pacific Islanders have tended to experience the highest rate of hepatitis B when compared with other ethnic groups. As such, rates of hepatitis B-related mortality remain higher among Asian/Pacific Islanders than among than their ethnic counterparts (CDC, 2020b).
- In 2018, the rate of tuberculosis among Asian people was 31 times higher than all people reported as having been diagnosed with tuberculosis nationwide (CDC, 2020b).
Black and Hispanic people and Alaska Natives experience worse health outcomes on several measures when compared with their White counterparts (NIH, 2023b):
- Alaska Natives, Hispanic people, and American Indians are at higher risk of being uninsured (Tolbert et al., 2022).
- Black, Hispanic, and Asian adults were less likely to receive care for mental health conditions as of 2021 (Hill et al., 2023).
- Approximately six in 10 Hispanic, Black, and Alaska Native adults did not receive a flu vaccine in the 2021–2022 flu season compared with less than one-half of White adults (Hill et al., 2023).
- Life expectancy at birth was shorter for Alaska Native people and Black people between 2019 and 2021 (Hill et al., 2023).
- In 2021, infant mortality rates were twice as high among Black people and Alaska Native people (Hill et al., 2023).
- In 2021, Black and Alaska Native women experienced the highest rates of death related to pregnancy (Hill et al., 2023).
- In 2021, Black and Hispanic children were more than twice as likely to experience food insecurity (Hill et al., 2023).
According to Healthy People 2030, approximately 38 percent of individuals living in the United States, age 18 and older, have undiagnosed prediabetes. The goal of this Healthy People 2030 objective is to decrease the proportion of American adults who have prediabetes from the baseline of 38 percent in 2013 to 33.2 percent by 2030. Healthy People 2030 discusses resources for individuals such as weight loss, healthy eating, and increased physical activity to reduce the risk of prediabetes.
According to the CDC (2022b; 2020c), African Americans, Hispanic/Latino Americans, and American Indians, Pacific Islanders, and some Asian Americans are at elevated risk of developing prediabetes.
(See Office of Disease Prevention and Health Promotion [ODPHP], 2023c.)
Read the scenario, and then answer the questions that follow.
Jose is a 53-year-old Hispanic male who has presented to the clinic with anxiety and with chest pain radiating to the right arm. Jose was recently let go from his job and has not been able to find employment. He is accompanied to the clinic by his wife and his mother. Jose indicates that he does not like coming to the doctor’s office, and he becomes more anxious as the nurse completes his health assessment. His vital signs are as follows:
- Blood Pressure: 126/82 mm Hg
- Respirations: 18 breaths/minute
- Heart Rate: 130 beats/minute
- Oxygen Saturation: 98 percent on room air
Other findings from the nurse’s health assessment of the client are as follows:
- Neurological: Within normal limits.
- Respiratory: Lungs clear to auscultation.
- Cardiovascular: Increased heart rate, but normal heart sounds. No peripheral edema noted.
- GI: Within normal limits.
- GU: Within normal limits.
- Pain: Radiating to the right arm 5 on a scale of 1–10.
Vulnerable Populations
According to the National Collaborating Centre for Determinants of Health (NCCDH), “vulnerability occurs when people are exposed to multiple layers of marginalization, including barriers to social, economic, political, and environmental resources that overlap to increase the risk of poor health. Individuals and communities are vulnerable to, live in vulnerable conditions or are forced into vulnerability rather than being labeled as vulnerable people/populations/groups” (NCCDH, 2023, para. 1). Ethnic and racial minorities are examples of vulnerable populations as many individuals within these groups are at risk of experiencing health disparities. Individuals experiencing poverty—many of whom identify as members of ethnic or racial minorities—are another demographic at risk of poor health outcomes related to lack of access to health care. For example, a 2020 report on income and poverty in the United States revealed the following (Shrider et al., 2021):
- Between 2019 and 2020, real median household income decreased 2.9 percent to $67,521.
- The total number of people with earnings decreased by 3.0 million, and the number of individuals who worked full-time year-round decreased by 13.7 million between 2019 and 2020.
- There was a 1.2 percent decrease in real median earnings for all workers.
- The official poverty rate increased from 10.5 percent in 2019 to 11.4 percent in 2020.
- In 2020, 37.2 million people were living in poverty, up from 33.9 million in 2019.
 The number of individuals identifying as lesbian, gay, bisexual, or transgender rose significantly between 2010 and 2020. As of 2017, there were approximately 11.4 to 12.2 million adults living in the United States who identified as lesbian, gay, bisexual, or transgender (National Library of Medicine, 2020).
The population of individuals with disabilities is another growing vulnerable population. Between 2008 and 2019, rates of disability among children under age 18 increased by 0.4 percent (Young & Crankshaw, 2021). Children who identified as American Indian and Alaskan Natives and those living in poverty had the highest rates of disability (Young & Crankshaw, 2021). In its Annual Report on People with Disabilities in America, the University of New Hampshire Institute on Disability (2023) states that the percentage of Americans with disabilities increased from 13.2 percent in 2019 to 13.5 percent in 2021.
For nurses and other health care professionals, these changing demographics are significant because they present challenges in areas across society, including in the workforce, education systems, and health care systems. Vulnerable populations tend to have more health issues such as preventable diseases (e.g., diabetes, hypertension, and obesity) and poor access to care, which leads to increased mortality (deaths) and morbidity rates (diseases). An increase in mortality and morbidity reflects increased health disparities (American Association of Colleges of Nursing, 2023). Members of the lesbian, gay, bisexual, transgender, queer/questioning, intersex, and asexual/aromantic/agender plus other unknowns ( LGBTQIA+ ) community—particularly youth—are at increased risk for negative health and life outcomes related to discrimination and stigma. The risk of suicide and substance misuse is high within this age group (CDC, 2023b). Individuals with disabilities are more likely to smoke and have obesity, heart disease, and diabetes. One in four adults in this population is also less likely to have a dedicated health care provider or receive an annual check-up (CDC, 2019a).
The World Health Organization (WHO) defines health inequities as “systematic differences in the health status of different population groups” (2023, para. 2). Health inequities are the result of human-made systems that favor one group over another. As a result, an unequal distribution of power occurs. The following have been identified as the structural root causes of health inequities: racism , sexism , classism , xenophobia , heterosexism , and ableism . These inequities can occur at the institutional level (how organizations treat others), interpersonal level (individuals’ behaviors toward each other), and the internal level (how individuals view themselves). Watch the video for more information about the causes of health inequities.
In addition to experiencing more health issues, members of underrepresented communities tend to distrust the health care system because of racism, bias , and perceived mistreatment. For example, in a Kaiser Family Foundation survey, 78 percent of individuals who identified as White said they trusted their doctors, although only 59 percent of those who identified as Black said they trusted theirs (Hamel et al., 2020).
As discussed in Structural Racism and Systemic Inequities, much of this distrust is due to systemic racism—the institutional unfair treatment of individuals based on race—and discrimination against racial minority populations in the United States. The perception by members of underrepresented communities that racism will be present often leads this population to choose not to seek health care. The resulting poor health outcomes further exacerbate health disparities between groups within a population.
Individuals tend to have better health outcomes when they receive care from providers who are familiar with their culture (Nair & Adetayo, 2019). Health care providers should work toward developing greater cultural competence —the ability to understand and work with people of cultures other than one’s own—which in turn increases trust within communities. The box below provides some suggestions for strategies nurses can use to increase client trust. Also see Culturally and Linguistic Responsive Nursing Care and Managing the Dynamics of Difference for more information on this topic.
- Learn about the client’s culture and ensure it is central in every aspect of the client’s care.
- Include the client and their family in the care process.
- Work to build trust with your client before and during the client care process.
- Be open and transparent with the client when communicating.
- Assess whether the client understands what you have taught them (health literacy).
- Be mindful of the degree to which the client has access to health care resources, and ensure you have mechanisms in place to address barriers, such as transportation, housing, and health insurance.
- Involve the interdisciplinary team in the client’s care to ensure all aspects of the client’s life and health issues are addressed. This would include professionals such as the physician, social workers, nutritionist, and health educators.
(See The Institute for Functional Medicine, 2023.)
Needed Policy Changes
To provide appropriate care to a changing population, policies and programs devoted to achieving health equity must be developed . Health equity refers to “the state in which everyone has a fair and just opportunity to attain their highest level of health” (CDC, 2022g, para. 1).
The CDC’s Office of Health Equity is on the front lines of achieving health equity through its CORE Strategy, which is an integration of health equity into every element of the work of the organization. CORE is an acronym for the following goals (CDC, 2023a):
- C ultivate Comprehensive Health Equity Science —The CDC Office of Health Equity will facilitate and accelerate the principles of health equity across all CDC programs, policies, and funding structures.
- O ptimize Interventions—The CDC Office of Health Equity will engage partners to address gender discrimination and gendered racism in the workplace.
- R einforce and Expand Robust Partnerships—The CDC Office of Health Equity will engage partners to mobilize around developing and implementing strategies to address health disparities and long-term health inequities, which includes the social determinants of health.
- E nhance Capacity and Workforce Engagement—The CDC Office of Health Equity will work to diversify the public health workforce.
One health policy with which most people are at least somewhat familiar is the Patient Protection and Affordable Care Act of 2010, also known as the Affordable Care Act (ACA). The primary goals of the ACA are to (U.S. Department of Health and Human Services [HHS], 2023a):
- Improve the affordability of health insurance to more individuals (Figure 5.3).
- Expand the Medicaid program, a state-operated health insurance program for those who are living in poverty or are disabled.
- Provide support for medical care delivery methods that are designed to yield lower health care costs.
This video provides a brief overview of the ACA, the 2010 law that increases health insurance options and provides additional health care rights and protections to all citizens, improving access and reducing disparities.
Watch the video, and then respond to the following questions.
- How does the ACA protect clients with preexisting medical conditions?
- What are some preventive services covered by the ACA? How do such services improve clients’ health?
Medicaid is a national program, jointly funded by each state and the Centers for Medicare and Medicaid Services (CMS, 2022), a federal agency. The program provides health coverage to the following populations: eligible low-income adults, children, pregnant clients, older adults, and people with disabilities. Medicaid is administered by individual states according to federal requirements. Each state independently determines its population’s Medicaid coverage and eligibility; to be eligible, an individual must fall within a certain financial category. One outcome of the ACA was to lower Medicaid eligibility requirements, thus increasing opportunities for those needing it; each state determined whether to expand Medicaid.
As of 2023, 38 out of 50 states and the District of Columbia had adopted and implemented expanded Medicaid; Wyoming, Kansas, Wisconsin, Texas, Mississippi, Tennessee, Alabama, Georgia, South Carolina, and Florida chose not to adopt Medicaid expansion, and South Dakota and North Carolina had adopted expansion but had not implemented it (Rudowitz et al., 2023). States that chose to expand Medicaid experienced an average reduction in poverty of 0.917 percent, or approximately 690,000 individuals lifted above the federal poverty line (Chee, 2019; Zewde & Wimer, 2019). These expansion states experienced increased state revenue as well as cost savings in other government programs that provide services that overlap with Medicaid (Guth & Ammula, 2021). Hospitals and other health care providers in expansion states have seen their profits and revenues increase (Guth & Ammula, 2021). In the states that have not adopted the Medicaid expansion, individuals fall into the coverage gap where their income is too high to qualify for Medicaid but too low to quality for subsidies offered by health insurance plans through the ACA Health Insurance Marketplace (Kagan, 2022). The uninsured rate in these states is almost double the rate of uninsured in states that have expanded Medicaid (15.4 percent compared with 8.1 percent) (Rudowitz et al., 2023). If all states adopted the Medicaid expansion, approximately 3.5 million uninsured adults would become eligible for coverage (Rudowitz et al., 2023).
Medicare , a federal health insurance program, provides health insurance coverage to individuals over age 65 and to those with specific disabilities who are younger than 65. Different parts of Medicare cover different services. Medicare Part A pays for inpatient hospital visits, skilled nursing facilities, hospice care, and some home health care; Part B pays for some outpatient care, doctor’s visits, and preventive services, and Part D covers the cost of prescription drugs (Medicare.gov, n.d.; Medicare Resources, 2023). Sixty-five million Americans receive insurance coverage through Medicare. This includes 57 million older adults and almost 8 million younger adults who have disabilities (Kaiser Family Foundation, 2023). Unlike Medicaid, Medicare is both funded and controlled by the federal government. To address the increasingly aging population—as well as increases in the number of individuals with disabilities—additional Medicare funding is necessary. By 2030, the percentage of American citizens who do not work and rely on those who are employed will exceed 70 percent. Medicare is expected to deplete its reserve by 2035 if the trend of the aging of America continues its current trajectory. In order for Medicare to continue providing for the growing number of recipients, policy change will be needed to fund the program.


5: Interactive Elements
The textbook of the future will be more than traditional textbooks of the past. The LibreText platform is designed to operate with this in mind with multiple interactive technologies available for integration to campus texts.
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- 5.2: Jupyter Notebooks (Executable Programming Code and Figures)
- CKEditor is a rich text editor which enables the user to write content directly inside web pages or online applications. Through the Binder Plugin, authors of textbooks have the option to include code within in their textbook pages to create a more interactive experience for their students. Currently the plugin supports Python 3, Julia, R, Octave, and SageMath. Additionally, all languages with the exception of SageMath support syntax highlighting for an easier scripting experience.
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- 5.2.1: How to Incorporate Data Files in Your Code Blocks- For C++
- 5.2.2: How to Incorporate Data Files in Your Code Blocks- For Julia
- 5.2.3: How to Incorporate Data Files in Your Code Blocks- For Octave
- 5.2.4: How to Incorporate Data Files in Your Code Blocks- For Python
- 5.2.5: How to Incorporate Data Files in Your Code Blocks- For R
- 5.2.6: How to Incorporate Data Files in Your Code Blocks- For SageMath
- 5.2.7: Installing custom packages
- <IP_ADDRESS>: Documentation of Supported Kernels
- 5.2.8: Using ipywidgets for Interactivity
- <IP_ADDRESS>: Enabling and Using Interactive Matplotlib Features
- <IP_ADDRESS>: Using ipyleaflet for Interactive Mapping
- <IP_ADDRESS>: Using ipyvolume for 3D plotting
- <IP_ADDRESS>: Using nglview to view molecular structures and trajectories
- <IP_ADDRESS>: Using pythreejs to generate and view three-dimensional models
- <IP_ADDRESS>: Using bqplot to make interactive plots
- <IP_ADDRESS>: Using IPyCytoscape to visualize graphs
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- 5.3: The Hypothesis Annotation System
- Hypothes.is is an open-source software project that aims to collect comments about statements made in any web-accessible content, and filter and rank those comments to assess each statement's credibility. It has been summarized as "a peer review layer for the entire Internet." The hypothesis system is native on all Libretexts libraries and can be accessed via the lurking buttons on the upper right of each page.
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- 5.7: Adding H5P (formative) Activities
- LibreTexts content can be enhanced with interactive H5P technology (https://h5p.org/). Currently this technology operates formatively (i.e., without a gradebook) within the LibreTexts platform, although efforts to expand the scope to summative activities are under development. The H5P activities are stored on a dedicated word-press server, not on the Library servers.
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- 5.8: H5P
- H5P is a free and open-source content collaboration framework based on JavaScript. H5P is an abbreviation for HTML5 and aims to make it easy for everyone to create, share and reuse interactive HTML5 content. The H5P infrastructure on the LibreTexts is part of the greater QUERY online assessment system that includes other online assessment technologies like WeBWorK.