91Ó°ÊÓ

In Exercises \(35-60\), find the reference angle for each angle. $$205^{\circ}$$

Use an identity to find the value of each expression. Do not use a calculator. $$\sec ^{2} \frac{\pi}{3}-\tan ^{2} \frac{\pi}{3}$$

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

Convert each angle in radians to degrees. Round to two decimal places. $$\frac{\pi}{13} \text { radians }$$

Find the exact value of each expression, if possible. Do not use a calculator. $$\tan \left(\tan ^{-1} 125\right)$$

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

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. $$d=3 \cos \left(\pi t+\frac{\pi}{2}\right)$$

Determine the amplitude and period of each function. Then graph one period of the function. $$y=5 \cos 2 \pi x$$

Find the exact value of each expression, if possible. Do not use a calculator. $$\tan \left(\tan ^{-1} 380\right)$$

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