91Ó°ÊÓ

In Exercises 25 to \(30,\) use a calculator to convert each DMS measure to its equivalent decimal degree measure. $$25^{\circ} 25^{\prime} 12^{\prime \prime}$$

Graph at least one full period of the function defined by each equation. $$y=4 \cos \frac{x}{2}$$

Graph at least one full period of the function defined by each equation. $$y=4 \sin \frac{2 \pi x}{3}$$

Use a calculator to find an approximate value of each function. Round your answers to the nearest ten-thousandth. $$\cos \left(-\frac{\pi}{5}\right)$$

Retail Sales The owner of a shoe store finds that the number of pairs of shoes \(S,\) in hundreds, that the store sells can be modeled by the function $$ S=2.7 \cos \left(\frac{\pi}{6} t-\frac{7}{12} \pi\right)+4 $$ where \(t\) is time measured in months, with \(t=0\) representing January 1 a. Find the phase shift and the period of \(S\). b. Graph one period of \(S\) c. Use the graph to determine in which month the store sells the most shoes.

A wheel is rotating at 50 revolutions per minute. Find the angular speed in radians per second.

Use a graphing utility to graph each function. $$y=\frac{1}{2} x \sin x$$

A car with a wheel of radius 14 inches is moving with a speed of 55 mph. Find the angular speed of the wheel in radians per second.

Graph \(y=e^{\sin x} .\) What is the maximum value of \(e^{\sin x} ?\) What is the minimum value of \(e^{\sin x} ?\) Is the function defined by \(y=e^{\sin x}\) a periodic function? If so, what is the period?

Each tire on a car has a radius of 15 inches. The tires are rotating at 450 revolutions per minute. Find the speed of the automobile to the nearest mile per hour.