91Ó°ÊÓ

In \(13-22\) , find the degree measure of each angle whose radian measure is given. \(\frac{7 \pi}{2}\)

In \(3-22 :\) a. Rewrite each function value in terms of its cofunction. b. Find, to four decimal places, the value of the function value found in a. $$ \cot 312^{\circ} $$

Complete the following table of cofunctions for radian values. $$ \begin{array}{|c|c|}\hline \text { Cofunctions (degrees) } & {\text { Cofunctions (radians) }} \\ \hline \cos \theta=\sin \left(90^{\circ}-\theta\right) & {\sin \theta=\cos \left(90^{\circ}-\theta\right)} & {} \\ \hline \tan \theta=\cot \left(90^{\circ}-\theta\right) & {\cot \theta=\tan \left(90^{\circ}-\theta\right)} & {} \\ \hline \sec \theta=\csc \left(90^{\circ}-\theta\right) & {\csc \theta=\sec \left(90^{\circ}-\theta\right)} & {} \\ \hline\end{array} $$

In \(24-32,\) find the exact value of each expression. $$ \cos \left(\arcsin \left(-\frac{\sqrt{3}}{2}\right)\right) $$

$$ \tan \left(-\frac{5 \pi}{3}\right) $$

The wheels on a bicycle have a radius of 40 centimeters. The wheels on a cart have a radius of 10 centimeters. The wheels of the bicycle and the wheels of the cart all make one complete revolution. a. Do the wheels of the bicycle rotate through the same angle as the wheels of the cart? Justify your answer. b. Does the bicvcle travel the same distance as the cart? Justify vour answer.

Latitude represents the measure of a central angle with vertex at the center of the earth, its initial side passing through a point on the equator, and its terminal side passing through the given location. (See the figure.) Cities A and \(\mathrm{B}\) are on a north-south line. City \(\mathrm{A}\) is located at \(30^{\circ} \mathrm{N}\) and City \(\mathrm{B}\) is located at \(52^{\circ} \mathrm{N}\) . If the radius of the earth is approximately \(6,400\) kilometers, find \(d\) , the distance between the two cities along the circumference of the earth. Assume that the earth is a perfect sphere.