91Ó°ÊÓ

Draw each of the following angles in standard position and then name the reference angle. $$311.7^{\circ}$$

Angle Between Cities Los Angeles and San Francisco are approximately 450 miles apart on the surface of the earth. Assuming that the radius of the earth is 4,000 miles, find the radian measure of the central angle with its vertex at the center of the earth that has Los Angeles on one side and San Francisco on the other side (Figure 15).

For each of the following angles, a. draw the angle in standard position. b. convert to radian measure using exact values. c. name the reference angle in both degrees and radians. $$ 30^{\circ} $$

Draw each of the following angles in standard position and then name the reference angle. $$-120^{\circ}$$

For each of the following angles, a. draw the angle in standard position. b. convert to radian measure using exact values. c. name the reference angle in both degrees and radians. $$ 260^{\circ} $$

Use the unit circle to evaluate each function. $$ \cot \frac{2 \pi}{3} $$

In the problems that follow, point \(P\) moves with angular velocity \(\omega\) on a circle of radius \(r\). In each case, find the distance \(s\) traveled by the point in time \(t\). \(\omega=5 \mathrm{rad} / \mathrm{sec}, r=4\) inches, \(t=2 \mathrm{sec}\)

Use the unit circle to find the six trigonometric functions of each angle. $$ \frac{7 \pi}{4} $$

If the distance to the sun is approximately 93 million miles, and, from the earth, the sun subtends an angle of approximately \(0.5^{\circ}\), estimate the diameter of the sun to the nearest 10,000 miles.

Use the unit circle to find all values of \(\theta\) between 0 and \(2 \pi\) for which the given statement is true. $$ \text { 30. } \csc \theta=1 $$