91Ó°ÊÓ

Graph two periods of the given cosecant or secant function. $$y=-\frac{1}{2} \csc \pi x$$

$$\text {use a calculator to find the value of the acute}\text { angle } \theta \text { to the nearest degree.}$$ $$\tan \theta=26.0307$$

Use an identity to find the value of each expression. Do not use a calculator. $$\csc ^{2} \frac{\pi}{6}-\cot ^{2} \frac{\pi}{6}$$

Find the exact value of each expression, if possible. Do not use a calculator. $$\tan ^{-1}\left[\tan \left(-\frac{\pi}{6}\right)\right]$$

In Exercises \(37-40,\) an object moves in simple harmonic motion described by the given equation, where \(t\) is measured in seconds and d in inches In each exercise, graph one period of the equation. Then find the following: a. the maximum displacement b. the frequency c. the time required for one cycle d. the phase shift of the motion. Describe how (a) through (d) are illustrated by your graph. $$d=-2 \sin \left(\frac{\pi t}{4}+\frac{\pi}{2}\right)$$

Find the exact value of each trigonometric function. Do not use a calculator. $$\cos \frac{9 \pi}{4}$$

In Exercises \(35-60\), find the reference angle for each angle. $$355^{\circ}$$

Convert each angle in radians to degrees. Round to two decimal places. -4.8 radians

$$\text {use a calculator to find the value of the acute}\text { angle } \theta \text { in radians, rounded to three decimal places.}$$ $$\cos \theta=0.4112$$

Determine the amplitude and period of each function. Then graph one period of the function. $$y=-4 \cos \frac{1}{2} x$$