11.9: Appraisal Methods
- Evaluate absolute appraisal methods
- Evaluate relative appraisal methods
- Discuss management by objectives
There are two primary methods for conducting performance appraisals: based on absolute or relative standards.
Absolute Appraisal Methods
Common methods of conducting an absolute appraisal are critical incident, BARS (Behaviorally Anchored Rating Scale), and a graphic rating scale.
Critical Incident
A critical incident appraisal focuses on the essential behaviors that determine whether a task is done well or poorly. Documentation in this case involves briefly summarizing situations (incidents) that demonstrate either successful or unsuccessful behavior and outcomes. The critical incident appraisal method is more intensive for the appraiser since it involves more attention to detail. This is especially the case since incidents should be recorded as they occur and be representative of the appraisal period rather than based on memory and written when preparing for the appraisal. However, this level of details if more valuable to an employee and may better support development. A variation on this is asking or tasking employees with recording their critical incidents, similar to a self-assessment.
Graphic Rating Scale
One of the simplest and most common appraisal methods is the graphic rating scale. A graphic rating performance appraisal form lists job behaviors, competencies, skills and results and provides five (more or less) rating options ranging from unsatisfactory to exceeds expectations. The appraiser selects a performance rating for each criteria and totals the values. The positive is rating scales are relatively easy to develop and complete and yield quantitative data that can be used to compare performance relative to prior appraisals or other employees. The downside is the method doesn’t provide a level of detail that supports specific corrective action. Another drawback: performance factors tend to be vague and open to interpretation—for example, quantity of work, quality of work, initiative—and performance ratings can be subjective.
BARS
The Behaviorally Anchored Rating Scale or BARS appraisal method combines aspects of the critical incident and graphic rating methods. Like the critical incident method, BARS focused on behaviors that constitute significant performance dimensions of a job. It differs from the typical graphic rating scale in that it focuses on job specifics rather than vague work statements. For example, instead of a rating that might be open to interpretation—for example, “Answers phone promptly and courteously”—a BARS approach would break it down into two component actions: “Answers phone within 3 rings.” and “Greets caller with “Hello. This is [name]. How may I help you?” [1]
Implementing BARS involves identifying the primary job behaviors and developing a 3–7 (or more) point rating scale that anchors the rating to specific descriptions of effective and ineffective behavior. The benefit of BARS is that it yields both qualitative and quantitative data. The quantitative data makes it possible to compare and rank relative employee performance. The level of detail in behavior descriptions also helps to avoid differences in interpretation across raters and employees. The downside of BARS is the complexity of development and maintenance, with each position requiring a set of evaluation criteria and rating descriptions.
| 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|
| Sometimes fails to follow doctors’ orders | Always follows doctors’ orders | Always follows doctors’ orders | Always follows doctors’ orders | Always follows doctors’ orders; available to meet with doctors whenever needed; |
| Often impatient with difficult patients | Occasionally impatient with difficult patients | Never impatient with difficult patients | Never impatient with difficult patients; helps other nurses with difficult patients | Never impatient with difficult patients; helps other nurses with difficult patients; ; eases patients’ fears |
| Doesn’t always follow hospital procedures | Rarely doesn’t follow hospital procedures | Always follows hospital procedures | Always follows hospital procedures | Always follows hospital procedures |
Relative Appraisal Methods
A second category of appraisal methods uses relative or comparative standards. Common methods in use include ranking and paired comparison and forced distribution.
Ranking
Ranking methods include individual ranking and group order ranking. These methods involve placing employees in relative performance (or perceived value) order from top to bottom or ranking them on a “curve” (bell curve). Group ranking—also referred to as stack ranking or forced distribution—involves placing employees in categories—for example, top 10% and bottom 10%. This practice was championed by former General Electric CEO Jack Welch, who imposed a 20/70/10 discipline where managers were forced to identify their top 10%, middle 70% and bottom 10% of employees annually. GE focused rewards and retention efforts on the top 10% and fired the bottom 10%.
According to Welch, “‘sprinkling’ financial rewards over a much larger group is a mistake.” Instead, the middle 70% should be coached and trained to move into the top 10%. [2] This technique was and remains controversial. A survey of human resource professionals surveyed “reported that forced ranking resulted in lower productivity, inequity and skepticism, negative effects on employee engagement, reduced collaboration, and damage to morale and mistrust in leadership.” [3] Human resource management perceptions are supported by field research. Wharton School of Management Associate Professor of Management Iwan Barankay’s research demonstrated that when people are rated relative to others, performance declined. Further, rating accuracy was questionable, with ratings having “as much to do with who the rater was (people gave higher ratings to those who were like them) as they did with performance.” [4]
Paired Comparison
The paired comparison method bases evaluations on an employee’s performance relative to his or her peers in selected job skill categories. For example, if you have five employees, you would compare their performance in each category individually, assigning a plus or a minus to indicate relative strength or weakness, as illustrated in Table 2. An employee’s evaluation would be the sum of their pluses and would be the basis of a relative ranking. This method is unwieldy for large numbers of employees and suffers from the vagueness and subjectivity of a graphic ranking system.
| Employees Rated | |||||
|---|---|---|---|---|---|
| Compared with | Employee HC | Employee SH | Employee AL | Employee DN | Employee ET |
| Employee HC | N/A | − | + | − | − |
| Employee SH | + | N/A | + | − | + |
| Employee AL | − | − | N/A | − | − |
| Employee DN | + | + | + | N/A | + |
| Employee ET | + | − | + | − | N/A |
Management by Objectives
An additional appraisal technique that represents a significant departure from the manager-centric approaches discussed above is a hybrid appraisal/management technique referred to as management by objectives (MBO). The MBO concept was introduced in management consultant, educator, and author Peter Drucker’s 1954 book The Practice of Management . What’s particularly powerful about using MBO is the clear connection between individual goals and organizational goals. The development of MBO is a process in which objectives “cascade down through the organization.” That is, “the organization’s overall objectives are translated into specific objectives for each succeeding level in the organization-divisional, departmental and individual.” [5]
A second key differentiating factor is the participative management aspect of MBO. Specifically, performance objectives (evaluation criteria) are discussed and agreed to by management and the employees. In theory, this approach results in employees who not only have a clearer understanding of expectations but greater buy-in. The greatest potential of MBO is developing goals and objectives that are aligned with not only the organization’s objectives but the employee’s personal goals and objectives.
Although MBO is a complex and time-consuming method that must be undertaken as an organizational initiative, it has the potential to address some of the relevance and motivation issues of other appraisal methods. DeCenzo, et. al. report that “studies of actual MBO programs confirm that MBO effectively increases employee performance and organizational productivity.” [6]
-
"
What is BARS (Behaviorally Anchored Rating Scale).
" The Performance Management and Appraisal Resource Center. Accessed August 20, 2019. ↵
-
Murray, Alan. "
Should I Rank My Employees?
" The Wall Street Journal. Accessed August 20, 2019. ↵
-
Ibid. ↵
-
Cappelli, Peter and Anna Tavis. "
The Performance Management Revolution
." Harvard Business Review. October 2016. Accessed August 20, 2019. ↵
-
DeCenzo, David A., Stephen P. Robbins, and Susan L Verhulst.
Fundamentals of Human Resource Management.
New York, NY: John Wiley & Sons, 2016. ↵
-
Ibid. ↵
Contributors and Attributions
- BARS for Army Nurses. Provided by : Open University of Hong Kong. Located at : http://www.opentextbooks.org.hk/ditatopic/32257# . Project : Human Resource Management. License : CC BY-SA: Attribution-ShareAlike
- Authored by : rawpixel. Provided by : Pixabay. Located at : pixabay.com/photos/boss-brainstorming-business-3385070/. License : Public Domain: No Known Copyright . License Terms : Pixabay License
- Authored by : geralt. Provided by : Pixabay. Located at : pixabay.com/photos/finger-feedback-confirming-3530353/. License : CC0: No Rights Reserved . License Terms : Pixabay License


38.1: Types of Skeletal Systems - Functions of the Musculoskeletal System
- Summarize the structure and role of the musculoskeletal system
The Musculoskeletal System
The musculoskeletal system provides support to the body and gives humans (and many animal species) the ability to move. The body’s bones (the skeletal system), muscles (muscular system), cartilage, tendons, ligaments, joints, and other connective tissue that supports and binds tissues and organs together comprise the musculoskeletal system.
Most importantly, the system provides form, support, stability, and movement to the body. For example, the bones of the skeletal system protect the body’s internal organs and support the weight of the body. The skeletal portion of the system serves as the main storage depot for calcium and phosphorus. It also contains critical components of the hematopoietic system (blood cell production). The muscles of the muscular system keep bones in place; they also play a role in movement of the bones by contracting and pulling on the bones, allowing for movements as diverse as standing, walking, running, and grasping items. To allow motion, different bones are connected by joints. Within these joints, bones are connected to other bones and muscle fibers via connective tissue such as tendons and ligaments. Cartilage prevents the bone ends from rubbing directly on each other. Muscles contract (bunch up) to move the bone attached at the joint.
Unfortunately, diseases and disorders that may adversely affect the function and overall effectiveness of the system exist and can be detrimental to the body. These potentially debilitating diseases can be difficult to diagnose due to the close relation of the musculoskeletal system to other internal systems. In humans, the most common musculoskeletal diseases worldwide are caused by malnutrition. Ailments that affect the joints, such as arthritis, are also widespread. These can make movement difficult; in advanced cases, they completely impair mobility. In severe cases in which the joint has suffered extensive damage, joint replacement surgery may be needed.
Progress in the science of prosthesis design has resulted in the development of artificial joints, with joint replacement surgery in the hips and knees being the most common. Replacement joints for shoulders, elbows, and fingers are also available. Even with this progress, there is still room for improvement in the design of prostheses. The state-of-the-art prostheses have limited durability, wearing out quickly, particularly in young or active individuals. Current research is focused on the use of new materials, such as carbon fiber, that may make prostheses more durable.
Key Points
- The skeleton, muscles, cartilage, tendons, ligaments, joints, and other connective tissues are all part of the musculoskeletal system, which work together to provide the body with support, protection, and movement.
- The bones of the skeletal system protect the body’s internal organs, support the weight of the body, and serve as the main storage system for calcium and phosphorus.
- The muscles of the muscular system keep bones in place; they assist with movement by contracting and pulling on the bones.
- To allow motion, different bones are connected by joints which are connected to other bones and muscle fibers via connective tissues such as tendons and ligaments.
- Cartilage prevents the bone ends from rubbing directly on each other.
- Malnutrition and arthritis are examples of disorders and diseases in the body that can severely impair the function of the musculoskeletal system.
Key Terms
- prosthesis : an artificial replacement for a body part, either internal or external
- arthritis : inflammation of a joint or joints causing pain and/or disability, swelling, and stiffness due to various causes, such as infection, trauma, degenerative changes, or metabolic disorders
- musculoskeletal system : an organ system made up of the muscular and skeletal systems; the system provides form, support, stability, and movement to the body


9.1.6: Marketing Strategy and the Marketing Plan
Learning Objectives
By the end of this section, you will be able to:
- Distinguish between a marketing strategy, a marketing plan, and a pitch
- Describe the elements of a marketing plan
Now that you have a better idea of what marketing is, you are ready to start developing a marketing strategy and plan. A marketing strategy describes how a company will reach consumers and convert them into paying customers. Having a solid-yet-flexible marketing strategy is a good business practice, no matter what kind of business you are in.
A marketing plan is a formal business document that is used as a blueprint or guide for how a company will achieve its marketing goals. A marketing plan differs from a business plan in that it focuses more on market research, attracting customers, and marketing strategies, whereas the business plan covers much more than that.
Marketing plans are important tools because they act as roadmaps for everyone involved in an enterprise. Writing a marketing plan forces you to specify goals and develop strategies to reach them, and encourages you to research markets and competition. A strong marketing plan will encourage entrepreneurs to think deeply about their business and profit potential, helping them make better business and marketing decisions. Additionally, a marketing plan can create greater involvement and cohesiveness among employees by clarifying goals and expectations.
A variety of marketing plan templates are available that can be modified to fit your business’s product and/or services. One thing to consider is why you are writing your plan and who your audience is. In addition to planning for your venture, will it be used by employees or potential investors? Different audiences will require different kinds of information. If it’s an employee, then you must include extra details about the operation of the business. If the plan is geared toward acquiring an investor, be sure to highlight the value that will be gained from investing.
Keep in mind that the various parts of a plan do not need to be written in a certain order. Plans should also be seen as flexible guides rather than absolute rules. All good marketing plans are living, breathing documents that help you measure success while allowing for course corrections when necessary. Table <IP_ADDRESS> provides the standard components of a marketing plan.
| Marketing Plan Section | Description and Purpose |
|---|---|
| Executive Summary | Provides a snapshot of the whole plan, including profit potential and major strategic ideas |
| Situation Analysis | Overviews internal and external environments related to the business and product; internal environments include company background and mission; external environments can include market needs, competition, market research, and an analysis of strengths, weaknesses, opportunities, and threats (SWOT) |
| Marketing Opportunity (Unmet Need, Proposed Solution, Value Proposition) | Validates the market opportunity being exploited by the business and articulates the potential gain for stakeholders |
| Business Model | Presents the framework for generation of sales and the business’s competitive advantage |
| Marketing Objectives | Specifies goals for sales (in units or dollars), market share growth, brand awareness, secured distribution channels, inventory, and pricing |
| Marketing Strategies | Explains target market, projected positioning, and strategies as they relate to the marketing mix (7Ps) |
| Action Program | Defines who will do what and when |
| Financials | Discloses sales estimates, projected budgets, and financials that will help readers understand the present and future economic condition of the company |
| Control Procedures | Describes procedures for measuring results, monitoring goals, and adapting the plan as needed |
Executive Summary
The executive summary is just that—a clear and concise summary of the major points of your marketing plan. Though it is placed first, it is generally written last because it is based on the information presented in other subsequent sections.
The executive summary is typically one or two pages long and includes key indicators of success for the business and its stakeholders, which may include company owners, managers, consultants, investors, and banks. Your goal is not merely to summarize everything in your plan but to highlight why people should be interested in your venture. Whether the reader is an employee or a potential partner or investor, the executive summary should seek to not only inform but to excite.
Focusing on the opportunity at hand, what makes your business model special, and the potential financial reward is a good way to capture a reader’s attention. For example, if your business’ strengths include a great marketing team and a significant competitive advantage, you should highlight them as reasons for success. Some readers may only read this section, so make sure you highlight what makes your company special and how you plan on turning that into profit.
Situation Analysis
In many ways, the basis of your marketing plan is found in your situation analysis , which is an examination of the internal and external circumstances relevant to your business and product. A good analysis will provide the logical support for the strategies you choose. For example, the research you conduct here explains why you will develop a certain product, how you will price it, and what you will do to reach your target market.
Good situation analyses often include a SWOT analysis, which looks at a company’s strengths, weaknesses, opportunities, and threats. They also look at future and current competitors, and include market validation research that has surveyed potential customers. This information is critical because it proves that you have done your due diligence on your product and market.
Marketing Opportunity
Assuming your background research has led you to determine that there is a business opportunity, this is where you explain what and where that opportunity is. For example, if your research led you to discover a gap in the market for educational children’s toys, this is where you explain the depth of the opportunity. Here you use your research as evidence to prove to your reader that there is a market gap and that you know how to fill it. If your goal is to get an investor interested, this is where you would let them know what they stand to gain and when they would gain that.
LINK TO LEARNING
The US Small Business Administration strives to help business owners initiate and succeed in developing enterprises. Their website is loaded with helpful information, classes, and templates that can help the entrepreneur navigate the intricacies of marketing, as well as provides helpful tips on developing a marketing plan.
Business Model
In this section, your job is to marry the opportunity you saw with the solution you have created. Here you articulate how your competitive advantage and points of differentiation (nature of the solution and its key features and benefits) will provide value to customers and earn profits that will sustain your business into the foreseeable future. What will you do to create value that attracts customers? How will you generate sales? Who is your target market? If you were opening a gym, this is where you would lay out how you will capture customers, the value they will receive, what types of membership contracts will be available to them, and so on.
A great tool for capturing this information is the Business Model Canvas. The nine building blocks of this model will help you to determine the targeted customer segment, value proposition that you will present each of your segments, channels for the distribution of the proposition or touchpoints, type of customer relationship you will build with your target, types of cost structures and revenue streams based on pricing means, and key resources, activities, and partners that will help you to succeed.
The canvas also allows the entrepreneur to innovate and to change if something doesn’t work out. The point of this tool is to put the pieces of a plan together.
Marketing Objectives
Here you present your specific goals and their tangible outcomes. It is not enough to say that you will be very successful without defining what exactly success means. The point of this section is to quantify your goals as units sold, sales/revenue, market share, or some other practical metric. Goals can also include creating measurable brand awareness and developing a certain number of distribution channels.
For example, good, measurable goals might be selling 300 units per month, selling $600,000 worth of product in a year, or gaining brand awareness of 10 percent of your target market in three months. Avoid goals that are unmeasurable or vague, as they won’t help you now or later.
No matter what your goals are, they should be reasonably achievable and as specific as possible. The reason for this is so that later on, you can determine whether you have been successful. If you haven’t, you will know something needs to change.
Marketing Strategies
As mentioned earlier, having a good marketing mix will help your business succeed. As an entrepreneur, you want to segment the market and figure out if there are possible pockets of people whom you can serve. The process of segmenting, targeting, and positioning (STP) will help you figure out who is your best customer and allow you to allocate your resources effectively to serve that market.
After going through this process, you can look at the marketing mix, and depending on whether you have a product, service, or a mixture of both, which is usually the case, you will outline your approach to the 7Ps of the marketing mix.
Action Plan
In the action plan, you detail how things will get done in your business on a day-to-day basis, when they will get done, and who will be doing them. Often, new business owners develop extensive strategies, but they don’t have the people power to implement them. Obviously, ensuring that you have the necessary human resources in place to execute your goals is important. This is the section where you make it clear that you do. For example, if you have a marketing team in place, highlighting their ability to execute your plans will help convince potential investors that you can put your plan into action.
Financials
Here you include budgets, forecasts, and any other information that will give readers and potential investors a clear picture of your business’s financial situation. Being transparent and truthful will create trust and goodwill between your company and potential investors.
This section is also important because it will help you determine how profitable your business might be. One place to start is by determining your expenses and future profits. Since most entrepreneurs tend to overestimate these numbers, it is best to develop financial projections for best- and worst-case scenarios, as well as a projection for an average case scenario.
Many entrepreneurs develop one-, three-, or five-year projections to get a sense of future profits and to prove that their business model is sustainable over the long run. Figure <IP_ADDRESS> provides an example.
Key Performance Indicators
Finally, you need to determine your key performance indicators, or how you will evaluate the effectiveness of your strategies, by looking at the progress you have made during a specific timeframe. These include the quantitative milestones that will tell you if you are on the right track, help you analyze your decision-making process and focus on specific strategies, and make changes if these don’t work.
For example, one of your milestones might be a sales goal of $50,000 within the first six months. If you are not on track by the time you hit this milestone, it can be an indication that you either overestimated your sales or your strategies are not working. In either case, you will need to make actionable steps to revise your projections or find more effective strategies.


2.4: The Appendicular Skeleton
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The appendicular skeleton includes the skeletal elements within the limbs, as well as supporting pectoral and pelvic girdles.
Learning Objectives
- List the components of the appendicular skeleton
Key Points
- The appendicular skeleton comprises 126 bones and is involved in locomotion and manipulation of objects in the environment.
- The bones of the appendicular skeleton are divided into two groups: the bones that are located within the limbs themselves, and the girdle bones that attach the limbs to the axial skeleton.
- The bones of the pectoral girdle anchor the upper limb to the thoracic cage of the axial skeleton.
- The pelvic girdle is formed by a single bone and serves as the attachment point for each lower limb.
Key Terms
- Girdle : A group of bones that connect the appendages to the axial skeleton.
- phalanges : The digital bones of the hands and feet (singular, phalanx).
- appendages : The parts of the body that extend from the axial trunk.
The appendicular skeleton of vertebrates, including humans, consists of the bones that support and compose the appendages (for example, the arms and legs of humans). The word appendicular is the adjective of the noun appendage.
The appendicular skeleton includes the skeletal elements within the limbs, as well as supporting the pectoral and pelvic girdles.
The appendicular skeleton comprises 126 bones and is involved in locomotion and manipulation of objects in the environment. It is unfused, allowing for greater range of motion.
Divisions of the Appendicular Skeleton
A diagram of the apendicular skeleton : Image depicting the human skeleton with the appendicular skeleton colored red.
The appendicular skeleton is divided into six major regions:
- The pectoral girdles consist of 4 bones: The left and right clavicle (2) and the scapula (2).
- The upper arms and forearms are made up of 6 bones: The left and right humerus (upper arm, 2), the ulna (2), and the radius (forearm, 2).
- The hands have 54 bones: The left and right carpals (wrist, 16), metacarpals (10), proximal phalanges (10), intermediate phalanges (8), and the distal phalanges (10).
- The pelvis has 2 bones: The left and right hip bone (2).
- The thighs and legs have 8 bones: The left and right femur (thigh, 2), patella (knee, 2), tibia (2) and fibula (leg, 2).
- The feet and ankles have 52 bones: The left and right tarsals (ankle, 14), metatarsals (10), proximal phalanges (10), intermediate phalanges (8), and distal phalanges (10).
Pectoral Girdle
The bones of the pectoral girdle consist of two bones (scapula and clavicle) and anchor the upper limb to the thoracic cage of the axial skeleton.
The three regions of the upper limb are: arm (humerus), forearm (ulna medially and radius laterally), and the hand.
The base of the hand contains eight bones (carpal bones), and the palm is formed by five bones (metacarpal bones). The fingers and thumb contain a total of 14 bones, called phalanges.
Pelvic Girdle
The pelvic girdle is formed by a single bone, the hip or coxal bone, and serves as the attachment point for each lower limb. Each hip bone is joined to the axial skeleton by its attachment to the sacrum of the vertebral column. The right and left hip bones attach to each other anteriorly.
The lower limb contains 30 bones and is divided into three regions, the thigh, leg, and foot. These consist of the femur, patella, tibia, fibula, tarsal bones, metatarsal bones, and phalanges.
- The femur is the single bone of the thigh.
- The patella (kneecap) articulates with the distal femur.
- The tibia is located on the medial side of the leg,
- The fibula is the thin bone of the lateral leg.
The bones of the foot are divided into three groups, the tarsal bones, metatarsal bones, and phalanges of the foot.
LICENSES AND ATTRIBUTIONS
CC LICENSED CONTENT, SHARED PREVIOUSLY
- Curation and Revision. Authored by : Boundless.com. Provided by : Boundless.com. License : CC BY-SA: Attribution-ShareAlike
CC LICENSED CONTENT, SPECIFIC ATTRIBUTION
- Human musculoskeletal system. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Human_m...keletal_system . License : CC BY-SA: Attribution-ShareAlike
- musculoskeletal system. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/musculoskeletal%20system . License : CC BY-SA: Attribution-ShareAlike
- red marrow. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/red%20marrow . License : CC BY-SA: Attribution-ShareAlike
- hematopoeisis. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/hematopoeisis . License : CC BY-SA: Attribution-ShareAlike
- Muscular System. Provided by : Wikipedia Commons. Located at : commons.wikimedia.org/wiki/File:Muscular_System.jpg . License : Public Domain: No Known Copyright
- Grey Skeleton. Provided by : PublicDomainPictures.net. Located at : http://www.publicdomainpictures.net/...=grey-skeleton . License : Public Domain: No Known Copyright
- Anatomical Terms of Bones. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Anatomical_terms_of_bone#Flat_bones . License : CC BY-SA: Attribution-ShareAlike
- Vertebral Column. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Vertebral_column . License : CC BY-SA: Attribution-ShareAlike
- Ossicles. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Ossicles . License : CC BY-SA: Attribution-ShareAlike
- Suture (Joint). Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Suture_(joint) . License : CC BY-SA: Attribution-ShareAlike
- Cranial Vault. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Cranial_vault . License : CC BY-SA: Attribution-ShareAlike
- Axial Skeleton. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Axial_skeleton . License : CC BY-SA: Attribution-ShareAlike
- Muscular System. Provided by : Wikipedia Commons. Located at : commons.wikimedia.org/wiki/File:Muscular_System.jpg . License : Public Domain: No Known Copyright
- Grey Skeleton. Provided by : PublicDomainPictures.net. Located at : http://www.publicdomainpictures.net/...=grey-skeleton . License : Public Domain: No Known Copyright
- Axial_skeleton_diagram.svg. Provided by : Wikipedian. Located at : en.Wikipedia.org/wiki/File:Axial_skeleton_diagram.svg . License : Public Domain: No Known Copyright
- The Appendicular Skeleton. Provided by : Open Stax College. Located at : http://openstaxcollege.org . License : CC BY: Attribution
- Appendicular Skeleton. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Appendicular_skeleton . License : CC BY-SA: Attribution-ShareAlike
- Muscular System. Provided by : Wikipedia Commons. Located at : commons.wikimedia.org/wiki/File:Muscular_System.jpg . License : Public Domain: No Known Copyright
- Grey Skeleton. Provided by : PublicDomainPictures.net. Located at : http://www.publicdomainpictures.net/...=grey-skeleton . License : Public Domain: No Known Copyright
- Axial_skeleton_diagram.svg. Provided by : Wikipedian. Located at : en.Wikipedia.org/wiki/File:Axial_skeleton_diagram.svg . License : Public Domain: No Known Copyright
- appendicular_skeleton_diagram.svg. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/File:A...on_diagram.svg . License : Public Domain: No Known Copyright


13.9: Introduction to Effects of Termination
What you’ll learn to do: Identify the legal and social effects of terminating an employee
As we discussed in the last section, there are a number of ways terminating employees impacts an organization. It is also important to remember that the terminated employee is heavily impacted. While we have discussed the side effects of terminations on the morale, productivity, and engagement in the workplace, there are a few other important ways that terminations can impact an organization. Legal ramifications from a poorly executed termination can have serious consequences. Understanding the legal and social impact of terminations will help companies to properly execute and plan for terminations.
This section will identify legal and ethical ways to terminate employees and the laws surrounding terminations. We will also discuss the advantages and disadvantages of laying off employees. Let’s get started!
Contributors and Attributions
- Introduction to Effects of Termination. Authored by : Freedom Learning Group. Provided by : Lumen Learning. License : CC BY: Attribution
- Authored by : Free-Photos. Provided by : Pixabay. Located at : pixabay.com/photos/conference-room-table-office-768441/. License : CC0: No Rights Reserved . License Terms : Pixabay License


5.1: The Ecological Niche
An important concept in ecology, which will be discussed in several contexts throughout the quarter is the ecological niche. A species’ ecological niche is the abiotic and biotic conditions the species requires in order to grow, reproduce, and survive. Every species, therefore, has a fundamental niche, which are the abiotic conditions the species can physiologically tolerate, as well as a realized niche, which is driven by species interactions. For example, consider a species of fish living in the ocean (Fig 5.1.1).
This species has certain physiological tolerances in temperature, salinity, etc, that determine where the species can exist. Each of the abiotic factors has an optimum range, where the species will be abundant. Outside of this optimum range (both above and below it), are zones of stress, where the species can survive, but experiences physiological stress and will be less common than in the optimum range. Beyond the zones of stress, are zones of intolerance, which represent conditions the species cannot tolerate and in which it will not be found. The tolerance ranges for all relevant abiotic conditions represent the species fundamental niche (Fig 5.1.2). Species interactions such as predation, parasitism, mutualisms, etc may result in this species not being found throughout its entire fundamental niche. For example, if this fish’s prey species do not occur in some areas of the fundamental niche, then this fish species may not occur there even though it could physiologically tolerate these conditions.
The example above illustrates how a species' realized niche might be reduced or contracted compared to the fundamental niche; however, species interactions can also expand the realized niche. For example, the resource acquisition section discussed root mutualisms that many plants form with mycorrhizal fungi and Rhizobium bacteria, which help the plant access soil nutrients. These mutualisms can expand the minimum soil nutrient availability in which the plant can survive, expanding its fundamental niche (Fig 5.1.3). We will consider the impact of species interactions on the niche in more detail in the species interactions sections.


4.5: Other Trigonometric Functions and Identities
- What are the other \(3\) trigonometric functions and how are they related to the cosine, sine, and tangent functions?
- How do the graphs of the secant, cosecant, and cotangent functions behave and how do these graphs compare to the cosine, sine, and tangent functions' graphs?
- What is a trigonometric identity and why are identities important?
The sine and cosine functions, originally defined in the context of a point traversing the unit circle, are also central in right triangle trigonometry. They enable us to find missing information in right triangles in a straightforward way when we know one of the non-right angles and one of the three sides of the triangle, or two of the sides where one is the hypotenuse. In addition, we defined the tangent function in terms of the sine and cosine functions, and the tangent function offers additional options for finding missing information in right triangles. We've also seeen how the inverses of the restricted sine, cosine, and tangent functions enable us to find missing angles in a wide variety of settings involving right triangles.
One of the powerful aspects of trigonometry is that the subject offers us the opportunity to view the same idea from many different perspectives. As one example, we have observed that the functions \(f(t) = \cos(t)\) and \(g(t) = \sin(t+\frac{\pi}{2})\) are actually the same function; as another, for \(t\) values in the domain \((-\frac{\pi}{2}, \frac{\pi}{2})\text{,}\) we know that writing \(y = \tan(t)\) is the same as writing \(t = \arctan(y)\text{.}\) Which perspective we choose to take often depends on context and given information.
While almost every question involving trigonometry can be answered using the sine, cosine, and tangent functions, sometimes it is convenient to use three related functions that are connected to the other three possible arrangements of ratios of sides in right triangles.
-
For any real number \(t\) for which \(\cos(t) \ne 0\text{,}\) we define the secant of \(t\text{,}\) denoted \(\sec(t)\text{,}\) by the rule
\[ \sec(t) = \frac{1}{\cos(t)}\text{.} \nonumber \]
-
For any real number \(t\) for which \(\sin(t) \ne 0\text{,}\) we define the cosecant of \(t\text{,}\) denoted \(\csc(t)\text{,}\) by the rule
\[ \csc(t) = \frac{1}{\sin(t)}\text{.} \nonumber \]
-
For any real number \(t\) for which \(\sin(t) \ne 0\text{,}\) we define the cotangent of \(t\text{,}\) denoted \(\cot(t)\text{,}\) by the rule
\[ \cot(t) = \frac{\cos(t)}{\sin(t)}\text{.} \nonumber \]
Note particularly that like the tangent function, the secant, cosecant, and cotangent are also defined completely in terms of the sine and cosine functions. In the context of a right triangle with an angle \(\theta\text{,}\) we know how to think of \(\sin(\theta)\text{,}\) \(\cos(\theta)\text{,}\) and \(\tan(\theta)\) as ratios of sides of the triangle. We can now do likewise with the other trigonometric functions:
\begin{align*} \sec(\theta) &= \frac{1}{\cos(\theta)} = \frac{1}{\frac{\text{adj}}{\text{hyp}}} = \frac{\text{hyp}}{\text{adj}}\\ \csc(\theta) &= \frac{1}{\sin(\theta)} = \frac{1}{\frac{\text{opp}}{\text{hyp}}} = \frac{\text{hyp}}{\text{opp}}\\ \cot(\theta) &= \frac{\cos(\theta)}{\sin(\theta)} = \frac{\frac{\text{adj}}{\text{hyp}}}{\frac{\text{opp}}{\text{hyp}}} = \frac{\text{adj}}{\text{opp}} \end{align*}
With these three additional trigonometric functions, we now have expressions that address all six possible combinations of two sides of a right triangle in a ratio.
Consider a right triangle with hypotenuse of length \(61\) and one leg of length \(11\text{.}\) Let \(\alpha\) be the angle opposite the side of length \(11\text{.}\) Find the exact length of the other leg and then determine the value of each of the six trigonometric functions evaluated at \(\alpha\text{.}\) In addition, what are the exact and approximate measures of the two non-right angles in the triangle?
Ratios in right triangles
Because the sine and cosine functions are used to define each of the other four trigonometric functions, it follows that we can translate information known about the other functions back to information about the sine and cosine functions. For example, if we know that in a certain triangle \(\csc(\alpha) = \frac{5}{3}\text{,}\) it follows that \(\sin(\alpha) = \frac{3}{5}\text{.}\) From there we can reason in the usual way to determine missing information in the given triangle.
It's also often possible to view given information in the context of the unit circle. With the earlier given information that \(\csc(\alpha) = \frac{5}{3}\text{,}\) it's natural to view \(\alpha\) as being the angle in a right triangle that lies opposite a leg of length \(3\) with the hypotenuse being \(5\text{,}\) since \(\csc(\alpha) = \frac{\text{hyp}}{\text{opp}}\text{.}\) The Pythagorean Theorem then tells us the leg adjacent to \(\alpha\) has length \(4\text{,}\) as seen in \(\triangle OPQ\) in Figure \(\PageIndex{3}\)
But we could also view \(\sin(\alpha) = \frac{3}{5}\) as \(\sin(\alpha) = \frac{\frac{3}{5}}{1}\text{,}\) and thus think of the right triangle has having hypotenuse \(1\) and vertical leg \(\frac{3}{5}\text{.}\) This triangle is similar to the originally considered \(3\)-\(4\)-\(5\) right triangle, but can be viewed as lying within the unit circle. The perspective of the unit circle is particularly valuable when ratios such as \(\frac{\sqrt{3}}{2}\text{,}\) \(\frac{\sqrt{2}}{2}\text{,}\) and \(\frac{1}{2}\) arise in right triangles.
Suppose that \(\beta\) is an angle in standard position with its terminal side in quadrant II and you know that \(\sec(\beta) = -2\text{.}\) Without using a computational device in any way, determine the exact values of the other five trigonmetric functions evaluated at \(\beta\text{.}\)
Properties of the secant, cosecant, and cotangent functions
Like the tangent function, the secant, cosecant, and cotangent functions are defined in terms of the sine and cosine functions, so we can determine the exact values of these functions at each of the special points on the unit circle. In addition, we can use our understanding of the unit circle and the properties of the sine and cosine functions to determine key properties of these other trigonometric functions. We begin by investigating the secant function.
Using the fact that \(\sec(t) = \frac{1}{\cos(t)}\text{,}\) we note that anywhere \(\cos(t) = 0\text{,}\) the value of \(\sec(t)\) is undefined. We denote such instances in the following table by “u”. At all other points, the value of the secant function is simply the reciprocal of the cosine function's value. Since \(|\cos(t)| \le 1\) for all \(t\text{,}\) it follows that \(|\sec(t)| \ge 1\) for all \(t\) (for which the secant's value is defined).
| \(t\) |
\(0\)
|
\(\frac{\pi}{6}\) | \(\frac{\pi}{4}\) | \(\frac{\pi}{3}\) | \(\frac{\pi}{2}\) | \(\frac{2\pi}{3}\) | \(\frac{3\pi}{4}\) | \(\frac{5\pi}{6}\) |
\(\pi\)
|
| \(\cos(t)\) | \(1\) | \(\frac{\sqrt{3}}{2}\) | \(\frac{\sqrt{2}}{2}\) | \(\frac{1}{2}\) | \(0\) | \(-\frac{1}{2}\) | \(-\frac{\sqrt{2}}{2}\) | \(-\frac{\sqrt{3}}{2}\) | \(-1\) |
| \(\sec(t)\) | \(1\) | \(\frac{2}{\sqrt{3}}\) | \(\sqrt{2}\) | \(2\) | u | \(-2\) | \(-\sqrt{2}\) | \(-\frac{2}{\sqrt{3}}\) | \(-1\) |
| \(t\) | \(\frac{7\pi}{6}\) | \(\frac{5\pi}{4}\) | \(\frac{4\pi}{3}\) | \(\frac{3\pi}{2}\) | \(\frac{5\pi}{3}\) | \(\frac{7\pi}{4}\) | \(\frac{11\pi}{6}\) | \(2\pi\) |
| \(\cos(t)\) | \(-\frac{\sqrt{3}}{2}\) | \(-\frac{\sqrt{2}}{2}\) | \(-\frac{1}{2}\) | \(0\) | \(\frac{1}{2}\) | \(\frac{\sqrt{2}}{2}\) | \(\frac{\sqrt{3}}{2}\) | \(0\) |
| \(\sec(t)\) | \(-\frac{2}{\sqrt{3}}\) | \(-\sqrt{2}\) | \(-2\) | u | \(2\) | \(\sqrt{2}\) | \(\frac{2}{\sqrt{3}}\) | \(1\) |
Table 4.5.4 and Table 4.5.5 help us identify trends in the secant function. The sign of \(\sec(t)\) matches the sign of \(\cos(t)\) and thus is positive in Quadrant I, negative in Quadrant II, negative in Quadrant III, and positive in Quadrant IV.
In addition, we observe that as \(t\)-values in the first quadrant get closer to \(\frac{\pi}{2}\text{,}\) \(\cos(t)\) gets closer to \(0\) (while being always positive). Since the numerator of the secant function is always \(1\text{,}\) having its denominator approach \(0\) (while the denominator remains positive) means that \(\sec(t)\) increases without bound as \(t\) approaches \(\frac{\pi}{2}\) from the left side. Once \(t\) is slightly greater than \(\frac{\pi}{2}\) in Quadrant II, the value of \(\cos(t)\) is negative (and close to zero). This makes the value of \(\sec(t)\) decrease without bound (negative and getting further away from \(0\)) for \(t\) approaching \(\frac{\pi}{2}\) from the right side. We therefore see that \(p(t) = \sec(t)\) has a vertical asymptote at \(t = \frac{\pi}{2}\text{;}\) the periodicity and sign behavior of \(\cos(t)\) mean this asymptotic behavior of the secant function will repeat.
Plotting the data in the table along with the expected asymptotes and connecting the points intuitively, we see the graph of the secant function in Figure \(\PageIndex{6}\)
We see from both the table and the graph that the secant function has period \(P = 2\pi\text{.}\) We summarize our recent work as follows.
For the function \(p(t) = \sec(t)\text{,}\)
- its domain is the set of all real numbers except \(t = \frac{\pi}{2} \pm k\pi\) where \(k\) is any whole number;
- its range is the set of all real numbers \(y\) such that \(|y| \ge 1\text{;}\)
- its period is \(P = 2\pi\text{.}\)
In this activity, we develop the standard properties of the cosecant function, \(q(t) = \csc(t)\text{.}\)
- Complete Table 4.5.8 and Table 4.5.9 to determine the exact values of the cosecant function at the special points on the unit circle. Enter “\(u\)” for any value at which \(q(t) = \csc(t)\) is undefined.
| \(t\) | \(0\) | \(\frac{\pi}{6}\) | \(\frac{\pi}{4}\) | \(\frac{4\pi}{3}\) | \(\frac{\pi}{2}\) |
\(\frac{2\pi}{3}\)
\(\frac{\sqrt{3}}{2}\) |
\(\frac{3\pi}{4}\)
\(\frac{\sqrt{2}}{2}\) |
\(\frac{5\pi}{6}\)
\(\frac{1}{2}\) |
\(\pi\)
\(0\) |
| \(\sin(t)\) | \(0\) | \(\frac{1}{2}\) | \(\frac{\sqrt{2}}{2}\) | \(-\frac{\sqrt{3}}{2}\) | \(1\) | ||||
| \(\csc(t)\) | \(\) | \(\) | \(\) | \(\) | \(\) | \(\) | \(\) | \(\) | \(\) |
| \(t\) | \(\frac{7\pi}{6}\) | \(\frac{5\pi}{4}\) | \(\frac{4\pi}{3}\) | \(\frac{3\pi}{2}\) | \(\frac{5\pi}{3}\) | \(\frac{7\pi}{4}\) | \(\frac{11\pi}{6}\) | \(2\pi\) |
| \(\sin(t)\) | \(-\frac{1}{2}\) | \(-\frac{\sqrt{2}}{2}\) | \(-\frac{\sqrt{3}}{2}\) | \(-1\) | \(-\frac{\sqrt{3}}{2}\) | \(-\frac{\sqrt{2}}{2}\) | \(-\frac{1}{2}\) | \(0\) |
| \(\csc(t)\) | \(\) | \(\) | \(\) | \(\) | \(\) | \(\) | \(\) | \(\) |
2. In which quadrants is \(q(t) = \csc(t)\) positive? negative?
3. At what \(t\)-values does \(q(t) = \csc(t)\) have a vertical asymptote? Why?
4. What is the domain of the cosecant function? What is its range?
5. Sketch an accurate, labeled graph of \(q(t) = \csc(t)\) on the axes provided in Figure 4.5.7, including the special points that come from the unit circle.
6. What is the period of the cosecant function?
In this activity, we develop the standard properties of the cotangent function, \(r(t) = \cot(t)\text{.}\)
- Complete Table 4.5.10 and Table 4.5.11 to determine the exact values of the cotangent function at the special points on the unit circle. Enter “u” for any value at which \(r(t) = \cot(t)\) is undefined.
| \(t\) | \(0\) | \(\frac{\pi}{6}\) | \(\frac{\pi}{4}\) |
\(\frac{\pi}{3}\)
\(\frac{\sqrt{3}}{2}\) \(\frac{1}{2}\) \(\frac{3}{\sqrt{3}}\) |
\(\frac{\pi}{2}\)
\(1\) \(0\) u |
\(\frac{2\pi}{3}\)
\(\frac{\sqrt{3}}{2}\) \(-\frac{1}{2}\) \(-\frac{3}{\sqrt{3}}\) |
\(\frac{3\pi}{4}\)
\(\frac{\sqrt{2}}{2}\) \(-\frac{\sqrt{2}}{2}\) \(-1\) |
\(\frac{5\pi}{6}\)
\(\frac{1}{2}\) \(-\frac{\sqrt{3}}{2}\) \(-\frac{1}{\sqrt{3}}\) |
\(\pi\)
\(0\) \(-1\) \(0\) |
| \(\sin(t)\) | \(0\) | \(\frac{1}{2}\) | \(\frac{\sqrt{2}}{2}\) | ||||||
| \(\cos(t)\) | \(1\) | \(\frac{\sqrt{3}}{2}\) | \(\frac{\sqrt{2}}{2}\) | ||||||
| \(\tan(t)\) | \(0\) | \(\frac{1}{\sqrt{3}}\) | \(1\) | ||||||
| \(\cot(t)\) |
| \(t\) | \(\frac{7\pi}{6}\) | \(\frac{5\pi}{4}\) | \(\frac{4\pi}{3}\) | \(\frac{3\pi}{2}\) | \(\frac{5\pi}{3}\) | \(\frac{7\pi}{4}\) | \(\frac{11\pi}{6}\) | \(2\pi\) |
| \(\sin(t)\) | \(-\frac{1}{2}\) |
\(-\frac{\sqrt{2}}{2}\)
|
\(-\frac{\sqrt{3}}{2}\) | \(-1\) | \(-\frac{\sqrt{3}}{2}\) | \(-\frac{\sqrt{2}}{2}\) | \(-\frac{1}{2}\) | \(0\) |
| \(\cos(t)\) | \(-\frac{\sqrt{3}}{2}\) |
\(-\frac{\sqrt{2}}{2}\)
|
\(-\frac{1}{2}\)
|
\(0\) | \(\frac{1}{2}\) | \(\frac{\sqrt{2}}{2}\) | \(\frac{\sqrt{3}}{2}\) | \(1\) |
| \(\tan(t)\) | \(\frac{1}{\sqrt{3}}\) | \(1\) | \(\frac{3}{\sqrt{3}}\) | u | \(-\frac{3}{\sqrt{3}}\) | \(-1\) | \(-\frac{1}{\sqrt{3}}\) | \(0\) |
| \(\cot(t)\) |
- In which quadrants is \(r(t) = \cot(t)\) positive? negative?
- At what \(t\)-values does \(r(t) = \cot(t)\) have a vertical asymptote? Why?
- What is the domain of the cotangent function? What is its range?
- Sketch an accurate, labeled graph of \(r(t) = \cot(t)\) on the axes provided in Figure \(\PageIndex{12}\) , including the special points that come from the unit circle.
6. On intervals where the function is defined at every point in the interval, is \(r(t) = \cot(t)\) always increasing, always decreasing, or neither?
7. What is the period of the cotangent function?
8. How would you describe the relationship between the graphs of the tangent and cotangent functions?
A few important identities
An identity is an equation that is true for all possible values of \(x\) for which the involved quantities are defined. An example of a non-trigonometric identity is
since this equation is true for every value of \(x\text{,}\) and the left and right sides of the equation are simply two different-looking but entirely equivalent expressions.
Trigonometric identities are simply identities that involve trigonometric functions. While there are a large number of such identities one can study, we choose to focus on those that turn out to be most useful in the study of calculus. The most important trigonometric identity is the fundamental trigonometric identity, which is a trigonometric restatement of the Pythagorean Theorem.
For any real number \(\theta\text{,}\)
\[ \cos^2(\theta) + \sin^2(\theta) = 1\text{.}\label{eq-fund-trig-identity}\tag{4.5.1} \]
Identities are important because they enable us to view the same idea from multiple perspectives. For example, the fundamental trigonometric identity allows us to think of \(\cos^2(\theta) + \sin^2(\theta)\) as simply \(1\text{,}\) or alternatively, to view \(\cos^2(\theta)\) as the same quantity as \(1 - \sin^2(\theta)\text{.}\)
There are two related Pythagorean identities that involve the tangent, secant, cotangent, and cosecant functions, which we can derive from the fundamental trigonometric identity by dividing both sides by either \(\cos^2(\theta)\) or \(\sin^2(\theta)\text{.}\) If we divide both sides of Equation (4.5.1) by \(\cos^2(\theta)\) (and assume that \(\cos(\theta) \ne 0\)), we see that
or equivalently,
A similar argument dividing by \(\sin^2(\theta)\) (while assuming \(\sin(\theta) \ne 0\)) shows that
These identities prove useful in calculus when we develop the formulas for the derivatives of the tangent and cotangent functions.
In calculus, it is also beneficial to know a couple of other standard identities for sums of angles or double angles. We simply state these identities without justification. For more information about them, see Section 10.4 in College Trigonometry , by Stitz and Zeager 1 .
http://stitz-zeager.com/
.
- For all real numbers \(\alpha\) and \(\beta\text{,}\) \(\cos(\alpha + \beta) = \cos(\alpha) \cos(\beta) - \sin(\alpha) \sin(\beta)\text{.}\)
- For all real numbers \(\alpha\) and \(\beta\text{,}\) \(\sin(\alpha + \beta) = \sin(\alpha) \cos(\beta) + \cos(\alpha) \sin(\beta)\text{.}\)
- For any real number \(\theta\text{,}\) \(\cos(2\theta) = \cos^2(\theta) - \sin^2(\theta)\text{.}\)
- For any real number \(\theta\text{,}\) \(\sin(2\theta) = 2\sin(\theta)\cos(\theta)\text{.}\)
In this activity, we investigate how a sum of two angles identity for the sine function helps us gain a different perspective on the average rate of change of the sine function.
Recall that for any function \(f\) on an interval \([a,a+h]\text{,}\) its average rate of change is
- Let \(f(x) = \sin(x)\text{.}\) Use the definition of \(AV_{[a,a+h]}\) to write an expression for the average rate of change of the sine function on the interval \([a+h,a]\text{.}\)
- Apply the sum of two angles identity for the sine function, \(\sin(\alpha + \beta) = \sin(\alpha) \cos(\beta) + \cos(\alpha) \sin(\beta)\text{,}\) to the expression \(\sin(a+h)\text{.}\)
-
Explain why your work in (a) and (b) together with some algebra shows that
\[ AV_{[a,a+h]} = \sin(a) \cdot \frac{\cos(h)-1}{h} - \cos(a) \frac{\sin(h)}{h}\text{.} \nonumber \]
-
In calculus, we move from
average
rate of change to
instantaneous
rate of change by letting \(h\) approach \(0\) in the expression for average rate of change. Using a computational device in radian mode, investigate the behavior of
\[ \frac{\cos(h)-1}{h} \nonumber \]
as \(h\) gets close to \(0\text{.}\) What happens? Similarly, how does \(\frac{\sin(h)}{h}\) behave for small values of \(h\text{?}\) What does this tell us about \(AV_{[a,a+h]}\) for the sine function as \(h\) approaches \(0\text{?}\)
Summary
-
The secant, cosecant, and cotangent functions are respectively defined as the reciprocals of the cosine, sine, and tangent functions. That is,
\[ \sec(t) = \frac{1}{\cos(t)}, \csc(t) = \frac{1}{\sin(t)}, \text{ and } \cot(t) = \frac{1}{\tan(t)}\text{.} \nonumber \]
-
The graph of the cotangent function is similar to the graph of the tangent function, except that it is decreasing on every interval on which it is defined at every point in the interval and has vertical asymptotes wherever \(\tan(t) = 0\) and is zero wherever \(\tan(t)\) has a vertical asymptote.
The graphs of the secant and cosecant functions are different from the cosine and sine functions' graphs in several ways, including that their range is the set of all real numbers \(y\) such that \(y \ge 1\) and they have vertical asymptotes wherever the cosine and sine function, respectively, are zero.
- A trigonometric identity is an equation involving trigonometric functions that is true for every value of the variable for which the trigonometric functions are defined. For instance, \(\tan^2(t) + 1 = \sec^2(t)\) for every real number \(t\) except \(t = \frac{\pi}{2} \pm k\pi\text{.}\) Identities offer us alternate perspectives on the same function. For instance, the function \(f(t) = \sec^2(t) - \tan^2(t)\) is the same (at all points where \(f\) is defined) as the function whose value is always \(1\text{.}\)
Exercises
Let \(\beta\) be an angle in quadrant II that satisfies \(\cos(\beta) = -\frac{12}{13}\text{.}\) Determine the values of the other five trigonometric functions evaluated at \(\beta\) exactly and without evaluating any trigonometric function on a computational device.
How do your answers change if \(\beta\) that lies in quadrant III?
For each of the following transformations of standard trigonometric functions, use your understanding of transformations to determine the domain, range, asymptotes, and period of the function, with careful justification. Then, check your results using Desmos or another graphing utility.
- \(\displaystyle f(t) = 5\sec(t-\frac{\pi}{2}) + 3\)
- \(\displaystyle g(t) = -\frac{1}{3}\csc(2t) - 4\)
- \(\displaystyle h(t) = -7\tan(t+\frac{\pi}{4}) + 1\)
- \(\displaystyle j(t) = \frac{1}{2}\cot(4t) - 2\)
In a right triangle with hypotenuse 1 and vertical leg \(x\text{,}\) with angle \(\theta\) opposite \(x\text{,}\) determine the simplest expression you can for each of the following quantities in terms of \(x\text{.}\)
- \(\displaystyle \sin(\theta)\)
- \(\displaystyle \sec(\theta)\)
- \(\displaystyle \csc(\theta)\)
- \(\displaystyle \tan(\theta)\)
- \(\displaystyle \cos(\arcsin(x))\)
- \(\displaystyle \cot(\arcsin(x))\)


10.3.2: Soil Moisture Seasons
Four soil moisture seasons can be defined by the soil moisture conditions.
Recharge
The recharge season is a time when water is added to soil moisture storage (+ΔST). The recharge period occurs when precipitation exceeds potential evapotranspiration but the soil has yet to reach its field capacity.
Surplus
The surplus season occurs when precipitation exceeds potential evapotranspiration and the soil has reached its field capacity. Any additional water applied to the soil runs off. If this water runs off into nearby streams and rivers it could cause flooding. Thus, the intensity (amount) and duration (length of season) of surplus can be used to predict the severity of potential flooding.
Utilization
The utilization season is a time when water is withdrawn from soil moisture storage (-ΔST). The utilization period occurs when potential evapotranspiration exceeds precipitation but soil storage has yet to reach 0 (dry soil).
Deficit
The deficit season occurs when occurs when potential evapotranspiration exceeds precipitation and soil storage has reached 0. This is a time when there is essentially no water for plants. Farmers then tap ground water reserves or water in nearby streams and lakes to irrigate their crops. Thus, the intensity (amount) and duration (length of season) of deficit can be used to predict the need for irrigation water.
Whether a place experiences all four seasons depends on the climate and soil properties. Wet climate and those places with soils having high field capacities are less likely to experience a deficit period. Likewise the duration and intensity of any season will be determined by the climate and soil properties. Given equal amounts of precipitation, coarse textured soils will generate runoff faster than fine textured soils and may experience more intense surplus


5.1: Activities Chapters 7, 9, 10, 11, 12, 13, 14, 16 - Construction Safety
Reflection: What tools and equipment do you use to do your work?
Were you trained on it's correct use? What type of physical hazard is present when using the tool or equipment? How do you manage or control the hazard? Consider guidance referenced in Tool and Shop Safety .
Flash Cards: Definitions and Key Terms
This interactive feature not available in print version of this workbook
Standard Mapping-Applying hierarchy of controls to tool and equipment standards in operating instructions and procedures
Standard Sections of interest
Review link to power tools and their associated specifications and if there is a link/pdf to operating instructions that as well. Look at clues from the specifications to determine what standards might be applicable regarding safe operation of the tools below and:
- List(code and what it says) them along with the potential hazard the regulation would address.
- Also note if you believe it is an engineering control or a work practice control. See Hierarchy of Controls .
- What PPE is most likely required?
Case Study-Fatality
The case below addresses a concern with the increased usage of rental equipment by individuals who have not had formal training on the proper and safe use of the equipment. In your discussion groups, identify the safety and health program failures that led to the worker fatality. This incident occurred at a private residence. How might the worksite have contributed to incident? How did the employer business practice contribute the fatality?
SUMMARY
A laborer working for a landscaping company died when he was pulled into a tree stump grinder. The victim was helping the landscaping company owner (stump grinder operator) guide the machine by pulling on a rope tied around his waist and attached to the stump grinder. The rope caught in the stump grinder’s grinding wheel and pulled the victim into its rotating motion.
Investigation
On April 9, 2018, at approximately 11:30 a.m., a 66-year-old Hispanic male laborer suffered fatal injuries while assisting a landscaping company owner who was operating a stump grinder. The employer of the victim was a family-owned and operated landscaping company that has been in business for over 20 years. According to the owner, he was the sole employee of the business. The employer occasionally hired the victim to help him with landscaping jobs. The employer spoke Spanish as his primary language, but also spoke and understood English. The victim was was a relative of the owner and had been working sporadically with him for about six months
The landscaping company did not have a written safety or Injury and Illness Prevention Program (IIPP) or any other safety documentation required by law. Neither the owner nor the victim had received formal training on the operation of stump grinders. Previously, they were provided with brief general instructions about stump grinder operation from the tool rental companies, but no specific instructions were given in this incident. The company owner was not trained in first aid or CPR.
The incident scene was a private residence located on a short cul-de-sac street. The residence was a two-story home with an attached garage. The tree involved in this incident was an approximately 50-foot sycamore in the front yard of the residence. Sycamore trees can grow to a height of 40 to 100 feet with a spread of 40 to 70 feet at maturity. Sycamores are often divided near the ground into a massive trunk with an aggressive root system that can be difficult to remove.
On the day of the incident, the owner and the victim attached a rope to an eye hook on the disc guard of the stump grinder (Exhibit 2) to help lower the machine below ground level to grind the stump and roots. The rope was not removed from the machine. The victim tied the rope around his waist, then pulled and leaned backward to help maneuver the grinding wheel while the owner was operating the stump grinder. A neighbor from across the street stated the victim was standing near the edge of the stump cavity. As the grinder was operating, the rope likely became slack and then caught around the grinding wheel, pulling the victim headfirst into the rotating disc.
Stump Grinder
A stump grinder is a power tool that removes tree stumps by means of a rotating grinding wheel with carbon steel teeth that chips away the wood. Stump grinders can be the size of a lawn mower or as large as a truck. Most accomplish their task by means of a high-speed disk cutter wheel with fixed carbon steel teeth that grinds the stump and roots into small chips. The grinding wheel movements are controlled by hydraulic cylinders that push the wheel laterally, and up and down, through the stump. Stump grinding is generally performed by a trained arborist or landscaper, but the machine may be rented by anyone from tool rental companies. The manufacturer’s instruction manual warns against allowing additional workers within 75 feet while grinding. There are various types of stump grinders, some of which are larger and could have better reached the stump and roots involved in this incident. If a stump grinder needs to be used to reach the roots below ground, a thorough job assessment should be performed to determine the proper machine that can reach the roots from above.
Reflection: What are the physics of electricity and electrical circuit parameters?
Which parameters are the primary focus of electrical safeguarding? Take a look at the label on the power supply for your laptop or other electronic device and list all safety certifications/symbols. Choose one of the OSHA Nationally Recognized Testing Laboratories (NRTLs) and provide details on its likely purpose for the device.
Flash Cards: Definitions and Key Terms
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Standard Mapping-Applying hierarchy of controls to electrical equipment and procedures
Portable fuel powered electric generators are increasingly used as back up power in homes and in commercial applications. However this equipment is also used on construction worksites by general and subcontractors. In this activity you will map construction safety standards to specific safety warnings and procedures for a portable generator. Choose 10 items from page 3 ( Important Safety Instructions) of the Ryobi Generator Safety Instructions and 10 items from page 4 (Specific Safety Rules) that map to the standards below and choose the standard section i.e. 1926.404 Wiring Design and Protection that the warning/procedure/rule is most likely associated with:
| Standard Subpart | Safety Procedure (pg 3)-Standard Section | Safety Rule(pg 4)-Standard Section |
|---|---|---|
| Example-1926 Subpart C-General Safety | Wipe spilled fuel from the unit-1926.24 | Save these instructions-1926.20 |
| Section 5(a)(1)-General Duty | ||
| 1926 Subpart C-General Safety and Health | ||
| 1926 Subpart D-Occupational Health | ||
| 1926 Subpart E-Personal Protective Equipment | ||
| 1926 Subpart F-Fire Protection and Prevention | ||
| 1926 Subpart G-Signs, Signals, Barricades | ||
| 1926 Subpart H-Materials Handling | ||
| 1926 Subpart I-Tools-Hand and Power | ||
| 1926 Subpart K-Electrical | ||
| 1926 Subpart AA-Confined Spaces in Construction |
Case study-fatality
Discuss in your group the specifics of the case below. Find three 29CFR1926 Subpart K standards not followed that appear to have contributed to this incident. Where on the hierarchy of controls are those standards? Discuss and debate how you would classify skills and training for electricians on the hierarchy of controls.
NIOSH FACE Report 2019-01
July 29, 2021
SUMMARY
On June 17, 2019, a 48-year-old city electric maintenance worker was electrocuted, while installing lines for security cameras along a residential area cul-de-sac. The electric maintenance worker arrived at the city workshop at 7 am and was instructed to install approximately 2,000 feet of triplex service wire on the light poles along a residential street for police surveillance cameras. The electric maintenance worker arrived at the work site at 10:24 am, with 2,000 feet of triplex service wire on a roll and placed the boom truck under light pole #1. He proceeded to install the triplex service wire on the first light pole connecting to light pole #2.  The 1,300 volt electric power lines running to the housing development were adjacent to the newly placed camera pole and beyond these lines were 3-phase 7,200 volt power lines. The electric maintenance worker got in the basket and raised it to approximately 28 feet. He began pulling some triplex service wire and installing it on the security pole. It is believed the worker did not realize his proximity to the power lines while performing this task and contacted his right shoulder with the energized power line. At 1:32 pm 911 was contacted because a residential home had experienced flickering lights and heard a loud noise. At the scene, the responders from the fire department found a truck with a raised basket in the air and a hard hat on the street. Once the fire department ladder truck was raised above the basket, the responders saw the electric maintenance worker laying on the floor of the basket. There was indication that a power line had arced, burnt through, and landed on the ground. The electric maintenance worker had signs of electrical burns on his right shoulder, hand, and clothing. He was pronounced dead on the scene at 2:28 pm.
Reflection: Scaffold vs Ladder
Create a list of activities or tasks that would require a ladder and scaffold, identify hazards and hazard categories associated with both types of safety equipment. Which piece of equipment requires more mental focus and effort during its use, in your opinion? Which leaves a worker more susceptible to mental and physical fatigue?
Flash Cards: Definitions and Key Terms
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Case study- Scaffold fatality
In your groups discuss the specifics of the case below. Identify the safety and health program failures. What specific scaffold safety standards were not followed? How are the social justice concerns discussed in Chapter 0 relevant to the incident below? What cultural issues may have played a part in the worker's death. Lastly, in many local, county, and state jurisdictions anyone performing construction type contract labor must be licensed to do so. How may a contractor license contribute to safer working conditions.
A day laborer fell approximately 12 feet off a scaffold at a private residence. The victim was applying a stone and stucco façade to the exterior of the home when the incident occurred. The victim was hired by the homeowner’s gardener from a street corner to perform the work. The victim rented, assembled, and was working from the scaffold when the incident occurred. The scaffold was erected without guardrails and the walk board was not secured. The victim was not wearing any type of fall protection.
Investigation
On Wednesday, January 12, 2011, at approximately 3:00 p.m., a 40-year-old Hispanic day laborer who worked as a construction worker died when he fell from a scaffold approximately 12 feet to the ground below. He was born in Mexico and completed nine years of education. The victim spoke only Spanish. The gardener who hired him also spoke Spanish, but the homeowner did not. The victim had worked in the Los Angeles area for the past five years. There was no documentation available to determine the victim’s experience or training in masonry. There was also no documentation available to determine the victim’s qualifications, training, or experience working with scaffolds.
The site of the incident was a private residence. The home owner had asked his gardener if he knew anyone who could reface the exterior of his home with a stone and stucco facade. The gardener hired the victim from a street corner to perform the work. The victim rented a scaffold from a local home improvement store and used it to access the exterior of the house. The victim rented five-foot scaffold frame sections, diagonal braces (two for each section), a walk board, and a side and end panel that were to be used as guard rails on the top section of the scaffold.
The victim erected the scaffold but it was leveled using improper methods. The walk board was not properly secured, and the guard rails on the top portion were not attached. He then used the scaffold to gain access to the upper portions of the home’s exterior wall. The victim was working alone off the scaffold walk board, approximately 12 feet above ground level and was not wearing any fall protection devices. The victim worked for two days performing the job. On the third day, he continued applying the stucco and stone façade. At one point, the victim reached for a cell phone that was being handed to him by the homeowner’s gardener. The walk board shifted and he fell off the scaffold to the ground below.
Reflection: Have you slipped, tripped or fallen lately?
Analyze your last misstep, slip, trip or outright fall. What were the surface conditions? What shoes were you wearing? What were you thinking about right before? Which condition or cause was most responsible for the misstep? How could it have been prevented?
Flash Cards-Definitions and Key Terms
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Case study- FAT/CAT Fall scenario development
Choose a fall fatality from the FAT/CAT . Create a plausible pre-fall scenario, precursor to the fall that may have realistically contributed to the fatality. What type of fall prevention methods would have prevented the death.
Reflection Aerial Lifts vs Personnel Lifts?
Conduct a search on Aerial Lift, Personnel Hoist, Personnel Lift. Describe what you find either by copy and paste of pictures or written descriptions of equipment. What are your observations? Why might they be associated with cranes?
Flash Cards-Key Terms and Definitions
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Case Study-Fatality
In your discussion group, identify the crane operator errors and the rigger/rigging errors. Which competent person do you believe was most at fault or bore the most responsibility? Which type of hazard resulted in the worker death, "struck by" or "caught in between/crushed by? In your opinion, what other issues are revealed in the summary?
Summary
In the summer of 2009, a 48-year-old male commercial roofer, working on a roof, died when a load of shrink-wrapped roofing material, weighing approximately 1,900 pounds fell 20-30 feet from a 40-inch by 50-inch wooden pallet being transported overhead by a tower crane. The decedent’s supervisor, who was the roof man (signal person) for the lift, was working in another area of the roof clearing space for the pallet of rolled roofing material to be placed. The rigger placed a ratchet strap around the roofing bundle, and then “basket-rigged” the wooden pallet with two slings, both of which were 28-foot long, 2-inch wide polyester slings. The slings were connected to a ½-inch by 19-foot 2-inch leg spreader equipped with 10-inch hooks and a master ring that was connected to the crane’s hook. The slings were placed through the fork lift sleeves of the pallet. The rolls of roofing material were not secured to the pallet. The rigger indicated the load was ready to be hoisted to the roof. As the rigger observed the load being raised, he did not note any load instability or imbalance. The crane operator lifted the load approximately 20-30 feet above roof level, and then began to transport the load to the placement area. This involved swinging the load over the area where the decedent and his coworkers had been assigned to work by the supervisor. The crane operator noticed the roofing rolls were beginning to fall from the pallet. The crane operator yelled out a warning to the workers. The rolls of roofing material fell from the pallet and struck the decedent. The coworkers called for emergency response, unhooked the ratchet strap, and removed the roofing materials from the decedent. Emergency response provided care, and the decedent was transported to a local hospital where he was declared dead.
Reflection: How is your driving record in construction road work zones?
Approximately 609 workers in road work zones were killed between 2011-2015. Share your observations and personal experiences from traveling through road work zones. How aware do you feel workers in those zones are of their surroundings?
Flash Cards: Definitions and key terms
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Video Traffic Control
Traffic Control Safety
Utililty Safety in Workzones
Traffic Control Devices
Case study-Traffic Control
The Manual on Uniform Traffic Control Devices (MUTCD) is incorporated by reference in the OSHA standards. In your discussion groups, identify any deficiencies you see in the control of the work zone where the fatality occurred. How could the flagger have been better protected?
New York Case Report 04NY012
Summary
On February 20 th , 2004 a 47 year-old male flagger, who was employed by a temporary employment service agency, was struck by a pickup truck driven by a traveling motorist in a highway work zone. At the time of the incident, the victim and another flagger were directing traffic on a state highway for a tree service crew that was trimming branches to clear the power lines that belonged to a local utility company. On the morning of the incident, the crew had closed two lanes of a three-lane highway and had left only one southbound driving lane open to all traffic, both northbound and southbound. Warning signs were placed ahead of the work zone at each end. The victim, who wore a reflective vest and a hard hat, was directing the southbound traffic with a “Stop/Slow” sign at the north end of the work zone. At approximately 9:05 a.m., a black pickup truck suddenly pulled out of the southbound traffic into the passing lane and accelerated to approximately 60 miles per hour (mph) into the work zone. The victim was struck by the vehicle and thrown in the air by the impact. He landed on the northbound shoulder approximately 30 feet from the collision point. The emergency squad and the New York State Police (NYSP) arrived at the incident site within minutes. The victim was transported by helicopter to a hospital trauma center where he died thirteen days after the incident from the injuries sustained in the collision. The driver of the pickup truck was arrested for multiple traffic violations.
The victim completed a flagger training course provided by the National Safety Council through the temporary employment service agency and became a certified flagger in January of 2004. According to the employment agency representative, the agency discussed general flagging safety with the flaggers, while worksite host employers at each specific site were responsible for site-specific safety. The employment agency issued the following personal protective equipment to the flaggers: ANSI certified reflective vests and hard hats.
Details of Investigation
The incident occurred on a major state highway that runs south to north from New York City to the New York State border with Canada. A local utility company contracted a tree service firm to trim branches and cut brush along the power lines adjacent to the highway. Two flaggers were hired from a temporary employment agency to direct traffic at the work site. The section where the tree trimming was taking place was a three-lane highway with one northbound and two southbound lanes. A double yellow line demarcated the northbound and southbound lanes. There was a solid white line on both sides of the highway and a dashed white line delineating the two southbound lanes. The roadway curved toward the east at both ends of the work zone. The speed limit in the area of the incident was 50 mph.
At the time of the incident, the victim was standing at the north end of the work zone in the closed southbound passing lane behind a line of traffic cones. He was directing the flow of the southbound traffic with a “Stop/Slow” sign. The victim communicated visually with the other flagger at the south end of the work zone. At approximately 9:05 a.m., the southbound traffic was slowly approaching the work zone. According to the traveling motorists who witnessed the incident, a black Ford F350 Super Duty Pickup truck suddenly pulled out of the traffic into the closed passing lane. The vehicle passed several vehicles that had slowed down in the open driving lane, and accelerated into the work zone. The victim ran towards the northbound lane to avoid the rapidly approaching vehicle. According to the NYSP collision reconstruction report, the pickup truck began braking at this point and then swerved into the northbound lane and struck the victim. The victim was thrown in the air by the impact and landed on the northbound shoulder approximately 30 feet from the collision point. The victim was taken to a hospital trauma center where he died on March 4 th from the injuries sustained in the collision.
Reflection:Excavation Hazards
All construction focus 4 hazards are present when excavation activities are underway. Choose one of the top five excavation hazards (cave-ins, water accumulation, underground utilities, falls, heavy equipment operations) and propose a focus 4 (falls, electrocution, struck by, caught in between/crushed by) safety protocol for addressing that hazard during excavation work.
Flash Cards: Definitions and key terms
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Case study- Excavation fatalities
Activity
Reference the handout for the case studies 13, 22, 31, 61 and cite 3 relevant regulations from the excavation standards that should have been followed in order to prevent the accidental death or injury in the case. Cite 2 other standards from another construction safety subpart that would have also been a factor in preventing the fatality.
Reflection: Ladder setup?
Have you ever setup and used a A-frame ladder or extension ladder? What was the reason? Recognizing that ladders are safety equipment and either used for access to higher level only, or access to higher level to perform a task, if you were to access the ladder to perform a task, what might that be? How does the requirement to maintain 3 points of contact and staying centered on the ladder impact your ability to do the task?
Flash Cards: Definitions and key terms
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Case study- Ladder Inspection
After watching the following Video-Ladder Safety 101, use the Cal/OSHA Ladder inspection guidelines to inspect a personal ladder or employer's ladder. Compare your inspection results with your discussion group members. What did you learn in performing the inspection? Identify two inspection requirements that are engineering controls and two that would be categorized as a work practice control.


11.14: Exercise- Improving the Referencing Script
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In this exercise, we’re going to make some improvements to the script from the previous exercise, including defining a variable for the name of the equations file and saving the dataset to your hard drive.
Make sure that MyScript4.m is still open. At the end of the set of lines that define the other folders and filenames, add this line:
Equations_filename = [DIR 'equations.txt'];
That line will create a variable that holds the path and filename of the file with the equations. It’s really easy to make an error when you create a variable like this. In fact, I initially made an error when I wrote that line of code. When you create a new variable for a path and filename, you should check it first before running your script. To do this, run that one line of code. (The DIR variable should already be set from when you ran the script earlier.) Then, type dir(Equations_filename ) on the command line. The dir command lists any files that match the variable you specify inside the parentheses. When you run this command, you should get an error message saying that the file is not found.
Now type Equations_filename on the command line to see the value of this variable. Do you see the problem? We’re missing the slash between the path and the filename (or a backslash on a Windows computer; see the text box below). Fix this by changing the code to:
Equations_filename = [DIR '/equations.txt'];
Now run that line of code and then the dir(Equations_filename ) command. If Equations_filename is set correctly, the dir command should just print the name of the file ( equations.txt ).
Now replace the string holding the path and filename in the pop_eegchanoperator command with Equations_filename so that the command looks like this:
EEG = pop_eegchanoperator( EEG, Equations_filename , 'ErrorMsg', 'popup', 'KeepChLoc', 'on', 'Warning', 'on' );
Quit EEGLAB, type clear all , and then save and run the updated script. It should lead to the same result as the previous version of the script that didn’t use the Equations_filename variable, but the script is now more robust.
Forward Slashes and Backslashes
Windows uses a backslash (\) to separate the elements of a path, whereas Mac OS, UNIX, and Linux use a forward slash (/). Matlab is smart enough to convert to the appropriate separator for your computer. I don’t really trust it, though, so I like to use a more explicit approach using a Matlab function named filesep . This function returns the appropriate file separator for the computer that the script is running on. For example, I would define the variable for the equations file as [DIR filesep 'equations.txt'] rather than [DIR '/equations.txt'] or [DIR '\equations.txt'] . If you type filesep on the command line, you’ll see that it returns ‘/’ if you’re running Mac OS, UNIX, or Linux and ‘\’ if you’re running Windows.
Let’s make a couple more improvements. First, when a script is running, you don’t usually want error and warning messages to appear as new windows that wait for you to respond. If you’re running a script overnight because it takes a long time, you don’t want the script to be waiting for a response to a warning message when you arrive the next morning. So, let’s change 'ErrorMsg', 'popup' parameters in the pop_eegchanoperator() function to 'ErrorMsg', 'cw' so that error messages are printed in the Command Window and change 'Warning', 'on' to 'Warning', 'off' so that warning messages aren’t printed. (But note that error messages will still be printed.)
Now let’s make some changes that will have a more direct impact. First, we’re going to add _ref to the end of the name of the dataset to indicate that the data have now been referenced. Type EEG.setname on the command line so that you can see what the current setname is. If Subject 10 is the active dataset, you should see that the setname is '10_N170' . To update the setname, add the following line to your script after the line with the pop_eegchanoperator command:
EEG.setname = [EEG.setname '_ref'];
This takes the current setname and appends _ref to the end, storing the result in the EEG.setname variable. That was pretty easy! Note that this is right before the line with the eeg_store command, so the new setname will be stored in ALLEEG and therefore appear in the Datasets menu once we get to the eeglab redraw command. This line of code violates my rule about using variables to define values, because I didn’t define a variable for '_ref' . Rules are made to be broken, but only when there’s a good reason. In this case, the '_ref' string is something that I always use, so putting it into the body of the script is unlikely to cause problems later.
Now let’s add some code for saving the referenced dataset to your hard drive, in the same folder as the original dataset. You should first use the GUI to save the current dataset on your hard drive so that you can use the history to see the command for saving a dataset file. Select EEGLAB > File > Save current dataset as , and use tmp.set as the filename (in the Chapter_11 folder). Because you’re running this routine to see the history, you don’t actually need the file, and this filename will help you remember that it’s a temporary file that you can delete at some point. Now type eegh to see the history. You should see something like this:
EEG = pop_saveset( EEG, 'filename','tmp.set','filepath','/Users/luck/Ch_10_Scripting/Exercises/');
Copy that line from the Command Window and paste it into your script after the line with the eeg_store command. But we want to make some changes before we use it. First, we don’t want the file to be named tmp.set . I like to have the filename be the same as the setname, but with .set on the end. To accomplish this, change the new line of code by replacing 'tmp.set' with [EEG.setname '.set'] (which creates a string with the setname followed by .set ).
We also want to change the path so that it uses the Subject_DIR variable we previously created to hold the path for this subject’s data. To do this, replace the string that currently lists the path (which is '/Users/luck/Ch_10_Scripting/Exercises/' on my computer but will be something else on your computer) to Subject_DIR . This line of code should now look like this:
EEG = pop_saveset( EEG, 'filename', [EEG.setname '.set'], 'filepath', Subject_DIR);
Before you run the code, I want to show you one more little trick for dealing with bugs and other kinds of errors. I probably made an error at least 50% of the time when I added code to one of the scripts for this book. If you have a script that loops through the data from 40 participants, it can be really annoying to have the script show an error message 40 times before it finishes. You can usually type ctrl-C to stop the code after the first error, but that doesn’t always work. So, the first time I try out a new script, I just try it with the data from the first participant. I do that by following the line that defines the subject IDs with another line that lists only the first subject ID. For example, near the top of MyScript4.m, I have these two lines:
SUB = [ 1 2 3 5 6 7 8 9 10 ]; %Array of subject numbers
%SUB = [ 1 ]; %Just the first subject
The first time I run the script after making a change, I simply remove the % symbol on the second of the two lines. This overwrites the original contents of SUB and replaces it with only the ID for Subject 1, and the loop runs only for this one subject. Once I get the script to work for that one subject, I then put the % symbol back and run the script again.
To see this in action, add the line with SUB = [ 1 ]; (without the % symbol). Now you can run the new version of the script that changes the setname and saves the dataset as a file. If you get an error, or it doesn't seem to work correctly, you can fix it and try again. Once you get the script to work without any problems, you can comment out that line (i.e., add the % symbol) and run the script again to process all the subjects.
Now you have a robust, well-designed script that loads the datasets, references the data, saves the referenced data to your hard drive, and makes the datasets available in the EEGLAB GUI. You can now open Script4b.m to see my version of this script. It has comments that explain each line of code.
Script4b.m also uses a slightly different version of the equations file, named Reference_Equations.txt , which reorders the channels in addition to referencing them. The order of the channels in the original data files reflects the order of electrodes in the BioSemi recording system we used to collect the data. This ordering is convenient for the process of placing the electrodes on the head, but not for viewing the data. I reordered the channels so that they are in sets that go from left to right for a given line of electrodes (e.g., F7, F3, Fz, F4, F8 for the Frontal channels).


3.12: End of Chapter Problems
Ions
1. Identify each as a cation, an anion, or molecule.
a. H +
b. Cl −
c. O 2
d. Ba 2 +
e. CH 4
f. CS 2
g. NH 3
h. Br −
i. H −
j. Hg 2 +
k. CCl 4
l. SO 3
2. What are ionophores? Explain how ionophores act as antibiotics.
Main Group Elements
1. Which of these ions is not likely to form?
a. Mg +
b. K +
c. S 3 −
d. N 3 −
2. When the following atoms become ions, what charges do they acquire?
a. Li
b. S
c. Ca
d. F
3. What characteristic charge do atoms in the first column of the periodic table have when they become ions?
4. What characteristic charge do atoms in the second column of the periodic table have when they become ions?
5. What characteristic charge do atoms in the third-to-last column of the periodic table have when they become ions?
6. What characteristic charge do atoms in the next-to-last column of the periodic table have when they become ions?
7. Starting with lithium and bromine atoms, use Lewis diagrams to show the formation of the ionic compound.
a. LiBr
b. MgO
Nomenclature of Ions
1. Name each ion.
a. Ca 2 +
b. S 2−
c. SO 4 2 −
d. NH 4 +
e. Ba 2 +
f. HCO 3 −
g. Ca 2 +
h. P 3−
i. H 2 PO 4 −
j. Sn 4 +
k. K +
l. Fe 3 +
m. HSO 4 −
n. Sn 2 +
o. Ca 2 +
p. S 2−
q. SO 3 2 −
r. NH 4 +
s. Cu +
t. Fe 2 +
2. Write the formula for each ion.
a. the bromide ion
b. the phosphate ion
c. the cupric ion
d. the magnesium ion
e. the fluoride ion
f. the carbonate ion
g. the ferrous ion
h. the potassium ion
i. the bromide ion
j. the phosphate ion
k. the cupric ion
l. the magnesium ion
m. the fluoride ion
n. the carbonate ion
o. the potassium ion
Formula of Ionic Compounds
1. Starting with lithium and bromine atoms, use Lewis diagrams to show the formation of the ionic compounds.
LiBr
MgO
2. Write the chemical formula for an ionic compound composed of each pair of ions.
a. the 3+ iron ion and the oxide ion
b. the calcium ion and the oxide ion
c. the 2+ copper ion and the sulfide ion
d. the 1+ copper ion and the sulfide ion
e. the potassium ion and the sulfate ion
f. the calcium ion and the nitrate ion
g. the magnesium ion and the carbonate ion
h. the aluminum ion and the acetate ion
i. the sodium ion and the sulfide ion
j. the aluminum ion and the fluoride ion
Nomenclature of Ionic Compounds
1. Name each ionic compound using both Stock and common systems if necessary.
Ca 3 (PO 4 ) 2
(NH 4 ) 2 Cr 2 O 7
KCl
CuCl
SnF 2
ZnBr 2
Fe(NO 3 ) 3
Al 2 O 3
CuF 2
AgF
Ca 3 (PO 4 ) 2
(NH 4 ) 2 Cr 2 O 7
KCl
CuCl
SnF 2
ZnBr 2
Fe(NO 3 ) 3
Al 2 O 3
CuF 2
AgF
2. Give two names for each compound
a. Al(HSO 4 ) 3
b. Mg(HSO 4 ) 2
c. Co(HCO 3 ) 2
d. LiHCO 3
Formula and Nomenclature of Ionic Compounds
Give the formula and the name of the ionic compound formed by each pair of ions. Use both the Stock and common systems, where appropriate.
a. Na + and Br −
b. Mg 2 + and Br −
c. Mg 2 + and S 2−
d. K + and Cl −
e. Mg 2 + and Cl −
f. Mg 2 + and F −
g. Na + and N 3−
h. Mg 2 + and N 3−
i. Al 3 + and S 2−
j. Li + and N 3−
k. Mg 2 + and P 3−
l. Li + and P 3−
m. Fe 3 + and Br −
n. Fe 2 + and Br −
o. Fe 3 + and S 2−
p. Cu + and S 2−
q. Cr 3 + and O 2−
r. Cr 2 + and O 2−
s. Pb 2 + and Cl −
t. Pb 4 + and Cl −
u. Cr 3 + and NO 3 −
v. Fe 2 + and PO 4 3 −
w. Ca 2 + and SO 4 2 −
x. Al 3 + and OH −
y. NH 4 + and NO 3 −
z. K + and SO 4 2 −
Covalent Bonds
Predict the number of covalent bonds formed by each nonmetal atom.
N
Cl
C
O
Br
H
Ionic vs. Molecular Compounds
1. Which compounds would you predict to be ionic? Circle.
a. Li 2 O
b. (NH 4 ) 2 S
c. CO 2
d. FeSO 3
e. C 6 H 6
f. C 2 H 6 O
g. Ba(OH) 2
h. CH 2 O
i. NH 2 CONH 2
j. (NH 4 ) 2 CrO 4
k. C 8 H 18
l. NH 3
2. Identify each compound as ionic or molecular.
a. Na 2 O
b. PCl 3
c. NH 4 Cl
d. OF 2
e. N 2 O
f. FeCl 3
g. (NH 4 ) 3 PO 4
h. SOCl 2
3. Is each compound formed from ionic bonds, covalent bonds, or both?
a. Na 2 O
b. Na 3 PO 4
c. N 2 O 4
d. Ba(OH) 2
e. F 2
f. PCl 3
4. Write the molecular formula for each compound.
- chlorine trifluoride
- phosphorus pentachloride
- sulfur dioxide
d. nitrogen dioxide
e. dioxygen difluoride
f. dinitrogen pentoxide
g. sulfur hexafluoride
h. nitrogen monoxide
5. Write the name for each compound.
- BrF 5
- S 2 F 2
- CO
d. CF 4
e. SeCl 2
f. SO 3
Formula Weight and Molecular Weight
1. Use the atomic weights rounded to two decimal places to determine the formula weight for each ionic compound.
- TiO 2
- AgBr
- Au(NO 3 ) 3
- Fe 3 (PO 4 ) 2
2. Calculate the molecular weight of each covalent compound? Use the atomic weights rounded to two decimal places.
a. C 2 H 2
b. CO
c. CO 2
d. BF 3
Mass-Mole Conversions
1. A biochemist needs 0.00655 mol of bilirubin (C 33 H 36 N 4 O 6 ) for an experiment. How many grams of bilirubin will that be?
2. A chemist needs 457.8 g of KMnO 4 to make a solution. How many moles of KMnO 4 is that?
3. What is the mass of 62.5 moles of carbon tetrachloride?
4. How many moles of ammonium hydroxide are present in 0.475 g?


2.25: Spiritual Health
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The spiritual dimension is understood to imply a phenomenon that is not material in nature, but belongs to the realm of ideas, beliefs, values and ethics that have arisen in the minds and conscience of human beings, particularly ennobling ideas. Ennobling ideas have given rise to health ideals, which have led to a practical strategy for Health for All that aims at attaining a goal that has both a material and non-material component. If the material component of the strategy can be provided to people, the non-material or spiritual one is something that has to arise within people and communities in keeping with their social and cultural patterns. The spiritual dimension plays a great role in motivating people’s achievement in all aspects of life.


17.2: Word Components Related to the Endocrine System
This section will describe common word components related to the endocrine system. These word components help build definitions for many medical terms. Other common prefixes are described in Chapter 1.3 , and common suffixes are described in Chapter 1.5.
Prefixes Related to the Endocrine System
- eu- : Good, normal
- hyper- : Above, excessive
- hypo- : Below, under, deficient
- oxy- : Rapid, sharp, acid
- pan- : All, total
- para- : Around, beside, beyond, abnormal
- poly- : Many or much
- syn- : Joined, together
- tetr- : Four
- tri- : Three
Word Roots With Combining Vowels Related to the Endocrine System
- acr /o: Extremities, height
- aden /o: Gland
- adren /o: Adrenal glands
- adrenal /o: Adrenal glands
- calc /i: Calcium
- cortic /o: Cortex, outer layer of a body organ
- dips /o: Thirst
- endocrin /o: Endocrine
- glyc /o: Sugar
- home /o: Sameness
- kal /i: Potassium
- myx /o: Mucus
- natr /o: Sodium
- parathyroid /o: Parathyroid gland
- phys /o: Growing
- pituitar /o: Pituitary gland
- somat /o: Body
- thyr /o: Thyroid gland
- thyroid /o: Thyroid gland
Suffixes Related to the Endocrine System
- -drome : Run, running together
- -ectomy : Excision, cut out
- -emia : In the blood
- -ia : Condition of, abnormal state, diseased state
- -ism : State of
- -itis : Inflammation
- -logist : Specialist who studies and treats
- -logy : Study of
- -megaly : Enlarged, enlargement
- -oid : Resembling
- -oma : Tumor
- -pathy : Disease
- -plasia : Condition of, formation, development, growth
- -tomy : Incision, cut into