4 secs. Calculate $h(t)$ for at least 8 values of $t$.\

[**2.9**]{}

Now let’s work out the equation for the tangent line to any power function. So let $y(x)=cx^{n}$ where c can be any constant and n is any positive integer. Write the tangent line, as before, $y_{t}(x) = a + bx$.\
(a) Find the value of $b$ at an arbitrary point $x_{0}$. (Hint: b will be a function of $c, n, and x_{0}$).\
(b) Now find the value of $a$ and write your expression for $y_{t}(x)$.\
(c) Check your result by letting $c$ and $n$ take the values used in the example.\

[**2.10**]{}

And, for an algebra brush-up, solve for t by completing the square $ at^{2} + bt +c = 0$. Show all of your work.

TRIGONOMETRIC FUNCTIONS
=======================

> ...they be crammin my mind with \[stuff\] they want us to remember, ... all kinds of crap like coaxiel coordinates, cosine computations, spheriod trigonometry, ...

-Winston Groom ([*Forrest Gump*]{})

In this section I present a novel (for an introductory textbook) discussion of the derivatives of the sine and cosine functions. Many students at this level have not learned to view the trigonometric functions as functions. I therefore begin 