91Ó°ÊÓ

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

\(\theta\) is an acute angle and sin u is given. Use the Pythagorean identity \(\sin ^{2} \theta+\cos ^{2} \theta=1\) to find cos \(\theta.\) $$ \sin \theta=\frac{7}{8} $$

Use a calculator to find the value of each expression rounded to two decimal places. $$ \sin ^{-1}(-0.625) $$

let \(\theta\) be an angle in standard position. Name the quadrant in which \(\theta\) lies. $$ \cot \theta>0, \quad \sec \theta<0 $$

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 time required for one cycle. $$ d=10 \cos 2 \pi t $$

In Exercises \(21-28,\) convert each angle in radians to degrees. $$ \frac{\pi}{9} $$

In Exercises 17–24, graph two periods of the given cotangent function. $$ y=-2 \cot \frac{\pi}{4} x $$

Determine the amplitude, period, and phase shift of each function. Then graph one period of the function. $$y=\frac{1}{2} \sin \left(x+\frac{\pi}{2}\right)$$

\(\theta\) is an acute angle and sin u is given. Use the Pythagorean identity \(\sin ^{2} \theta+\cos ^{2} \theta=1\) to find cos \(\theta.\) $$ \sin \theta=\frac{\sqrt{39}}{8} $$

Use a calculator to find the value of each expression rounded to two decimal places. $$ \cos ^{-1} \frac{3}{8} $$