# Homework 7

Due Thursday, May, 11:

The following problems must be turned in (but will not be graded for correctness):

1. Prove the following identity: $\frac{1}{1 - sin x} - \frac{1}{1 + sin x} = 2tan x sec x$.
2. Evaluate $\mathrm{cos}(\mathrm{tan}^{-1}(\sqrt{3}))$ and $\mathrm{sec}(\mathrm{tan}^{-1}(x))$.
3. Is there any real number x where $\mathrm{sec}(\mathrm{tan}^{-1}(x))$ is negative? Explain why or why not, making reference to the unit circle.
4. Convert the following radian measures to degrees: $3\pi/4, 4\pi/3, 5\pi/6$.

The following problems will be graded and will account for 30% of this homework’s grade:

1. Graph $y = 3\mathrm{sin}(2x)$ on the interval $[0, 2\pi]$.
2. Let $f(x) = \frac{1}{x - 3}$. Find and simplify $\frac{f(a+h) - f(a)}{h}$, assuming h is not 0.
3. Graph $y = 2^{-x} - 1$, making sure to label any intercepts and asymptotes.

The following problems are optional, and need not be turned int:

Section 5.3 #47-50

Section 5.4 #19-20, 25, 35-38

Section 5.5 #3-6, 41-46

Section 7.1 #35, 39, 48