### Review Exercises

## Angles

For the following exercises, convert the angle measures to degrees.

$-\frac{5\pi}{3}$

For the following exercises, convert the angle measures to radians.

$\mathrm{180\xb0}$

Find the length of an arc in a circle of radius 7 meters subtended by the central angle of $\mathrm{85\xb0}.$

Find the area of the sector of a circle with diameter 32 feet and an angle of $\frac{3\pi}{5}$ radians.

For the following exercises, find the angle between $\mathrm{0\xb0}$ and $\text{360\xb0}$ that is coterminal with the given angle.

$\mathrm{-80\xb0}$

For the following exercises, find the angle between 0 and $2\pi $ in radians that is coterminal with the given angle.

$\frac{14\pi}{5}$

For the following exercises, draw the angle provided in standard position on the Cartesian plane.

$\mathrm{75\xb0}$

$-\frac{\pi}{3}$

Find the linear speed of a point on the equator of the earth if the earth has a radius of 3,960 miles and the earth rotates on its axis every 24 hours. Express answer in miles per hour. Round to the nearest hundredth.

A car wheel with a diameter of 18 inches spins at the rate of 10 revolutions per second. What is the car's speed in miles per hour? Round to the nearest hundredth.

## Right Triangle Trigonometry

For the following exercises, use side lengths to evaluate.

$\mathrm{cot}\phantom{\rule{0.3em}{0ex}}\frac{\pi}{3}$

$\mathrm{cos}\left(\frac{\pi}{2}\right)=\mathrm{sin}\left(\_\_\_\xb0\right)$

For the following exercises, use the given information to find the lengths of the other two sides of the right triangle.

$\mathrm{cos}\phantom{\rule{0.3em}{0ex}}B=\frac{3}{5},a=6$

For the following exercises, use Figure 1 to evaluate each trigonometric function.

$\mathrm{sin}\phantom{\rule{0.3em}{0ex}}A$

For the following exercises, solve for the unknown sides of the given triangle.

A 15-ft ladder leans against a building so that the angle between the ground and the ladder is $\mathrm{70\xb0}.$ How high does the ladder reach up the side of the building? Find the answer to four decimal places.

The angle of elevation to the top of a building in Baltimore is found to be 4 degrees from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the building. Find the answer to four decimal places.

## Unit Circle

Find the exact value of $\mathrm{sin}\phantom{\rule{0.3em}{0ex}}\frac{\pi}{3}.$

Find the exact value of $\mathrm{cos}\phantom{\rule{0.3em}{0ex}}\pi .$

State the reference angle for $\frac{3\pi}{4}.$

Compute sine of $\frac{5\pi}{4}.$

State the range of the sine and cosine functions.

## The Other Trigonometric Functions

For the following exercises, find the exact value of the given expression.

$\mathrm{tan}\phantom{\rule{0.3em}{0ex}}\frac{\pi}{4}$

$\mathrm{sec}\phantom{\rule{0.3em}{0ex}}\frac{\pi}{4}$

For the following exercises, use reference angles to evaluate the given expression.

$\mathrm{sec}\phantom{\rule{0.3em}{0ex}}\mathrm{315\xb0}$

If $\text{tan}(t)=\mathrm{-0.6},$ what is the $\text{tan}(-t)?$

If $\text{cos}(t)=\frac{\sqrt{2}}{2},$ find $\text{sin}(t+2\pi ).$ There are two possible solutions.

Which trigonometric functions are odd?