91Ó°ÊÓ

Express the exact value of each function as a single fraction. Do not use a calculator. $$\text { If } \theta \text { is an acute angle and } \cot \theta=\frac{1}{4}, \text { find } \tan \left(\frac{\pi}{2}-\theta\right)$$

A boat leaves the entrance to a harbor and travels 40 miles on a bearing of \(\mathrm{S} 64^{\circ} \mathrm{E}\). How many miles south and how many miles east from the harbor has the boat traveled?

Graph two periods of each function. $$y=\left|\tan \frac{1}{2} x\right|$$

Find the exact value of each trigonometric function. Do not use a calculator. $$\cos \left(-\frac{\pi}{4}-2000 \pi\right)$$

Express the exact value of each function as a single fraction. Do not use a calculator. $$\text { If } \theta \text { is an acute angle and } \cos \theta=\frac{1}{3}, \text { find } \csc \left(\frac{\pi}{2}-\theta\right)$$

In Exercises \(47-62,\) use a sketch to find the exact value of each expression. $$\cos \left[\sin ^{-1}\left(-\frac{4}{5}\right)\right]$$

Determine the amplitude, period, and phase shift of each function. Then graph one period of the function. $$y=3 \cos (2 \pi x+4 \pi)$$

In Exercises \(35-60,\) find the reference angle for each angle. $$553^{\circ}$$

In Exercises \(47-62,\) use a sketch to find the exact value of each expression. $$\sin \left(\cos ^{-1} \frac{\sqrt{2}}{2}\right)$$

Let \(f(x)=2 \sec x, g(x)=-2 \tan x,\) and \(h(x)=2 x-\frac{\pi}{2}\). Graph two periods of $$y=(f \circ h)(x)$$.