91Ó°ÊÓ

In Exercises \(23-34\), find the exact value of each of the remaining trigonometric functions of \(\theta\). \(\sin \theta=-\frac{12}{13}, \quad \theta\) in quadrant III

Determine the amplitude, period, and phase shift of each function. Then graph one period of the function. $$y=-2 \sin \left(2 x+\frac{\pi}{2}\right)$$

Find a cofunction with the same value as the given expression. $$\tan \frac{\pi}{9}$$

In Exercises \(23-34\), find the exact value of each of the remaining trigonometric functions of \(\theta\). \(\sin \theta=\frac{5}{13}, \quad \theta\) in quadrant II

Convert each angle in radians to degrees. $$\frac{7 \pi}{6}$$

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, find the following: a. the maximum displacement b. the frequency c. the lime required for one cycle. $$d=\frac{1}{2} \sin 2 t$$

Sin \(t\) and cos \(t\) are given. Use identities to find tan \(t,\) csc \(t,\) sec \(t,\) and cot \(t .\) Where necessary, rationalize denominators. $$\sin t=\frac{8}{17}, \cos t=\frac{15}{17}$$

In Exercises \(19-30,\) use a calculator to find the value of each expression rounded to two decimal places. $$\cos ^{-1} \frac{\sqrt{5}}{7}$$

Find a cofunction with the same value as the given expression. $$\tan \frac{\pi}{7}$$

Determine the amplitude, period, and phase shift of each function. Then graph one period of the function. $$y=-3 \sin \left(2 x+\frac{\pi}{2}\right)$$