91Ó°ÊÓ

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

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

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

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

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 $$y=(f \circ h)(x)$$

A forest ranger sights a fire directly to the south. A second ranger, 7 miles east of the first ranger, also sights the fire. The bearing from the second ranger to the fire is \(\mathrm{S} 28^{\circ} \mathrm{W}\). How far, to the nearest tenth of a mile, is the first ranger from the fire?

In Exercises \(35-60\), find the reference angle for each angle. $$\frac{17 \pi}{6}$$

Use a vertical shift to graph one period of the function. $$y=\sin x+2$$

Use a sketch to find the exact value of each expression. $$\cos \left(\sin ^{-1} \frac{1}{2}\right)$$