91Ó°ÊÓ

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. $$ d=-6 \cos 2 \pi t $$

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

In Exercises \(21-28,\) convert each angle in radians to degrees. $$ \frac{2 \pi}{3} $$

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

In Exercises 17–24, graph two periods of the given cotangent function. $$ y=3 \cot \left(x+\frac{\pi}{4}\right) $$

find the exact value of each of the remaining trigonometric functions of \(\theta\) $$ \sin \theta=-\frac{12}{13}, \quad \theta \text { in quadrant III } $$

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

In Exercises \(21-28,\) convert each angle in radians to degrees. $$ \frac{3 \pi}{4} $$

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. $$ d=-8 \cos \frac{\pi}{2} t $$

Use a calculator to find the value of each expression rounded to two decimal places. $$ \cos ^{-1} \frac{4}{9} $$