91Ó°ÊÓ

7–52 Find the period and graph the function. $$y=\csc \left(x-\frac{\pi}{2}\right)$$

7–52 Find the period and graph the function. $$y=\sec \left(x+\frac{\pi}{4}\right)$$

An initial amplitude \(k,\) damping constant \(c,\) and frequency \(f\) or period \(p\) are given. (Recall that frequency and period are related by the equation \(f=1 / p . )\) (a) Find a function that models the damped harmonic motion. Use a function of the form \(y=k e^{-c t} \cos \omega t\) in Exercises \(17-20,\) and of the form \(y=k e^{-c t}\) sin \(\omega t\) in Exercises \(21-24\). (b) Graph the function. $$k=0.75, \quad c=3, \quad p=3 \pi$$

Find the exact value of the trigonometric function at the given real number. $$ \begin{array}{llll}{\text { (a) } \sec (-\pi)} & {\text { (b) } \sec \pi} & {\text { (c) } \sec 4 \pi}\end{array} $$

Find the amplitude and period of the function, and sketch its graph. $$ y=5 \cos \frac{1}{4} x $$

Find the exact value of the trigonometric function at the given real number. $$ \begin{array}{llll}{\text { (a) } \sin 13 \pi} & {\text { (b) } \cos 14 \pi} & {\text { (c) } \tan 15 \pi}\end{array} $$

Find the amplitude and period of the function, and sketch its graph. $$ y=-\frac{1}{3} \cos \frac{1}{3} x $$

7–52 Find the period and graph the function. $$y=\cot \left(x+\frac{\pi}{4}\right)$$

\(21-30=\) Find the terminal point \(P(x, y)\) on the unit circle determined by the given value of \(t .\) $$ t=\frac{\pi}{2} $$

An initial amplitude \(k,\) damping constant \(c,\) and frequency \(f\) or period \(p\) are given. (Recall that frequency and period are related by the equation \(f=1 / p . )\) (a) Find a function that models the damped harmonic motion. Use a function of the form \(y=k e^{-c t} \cos \omega t\) in Exercises \(17-20,\) and of the form \(y=k e^{-c t}\) sin \(\omega t\) in Exercises \(21-24\). (b) Graph the function. $$k=7, \quad c=10, \quad p=\pi / 6$$