91Ó°ÊÓ

\(21-30=\) Find the terminal point \(P(x, y)\) on the unit circle determined by the given value of \(t .\) $$ t=\frac{3 \pi}{2} $$

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. $$k=1, \quad c=1, \quad p=1$$

7–52 Find the period and graph the function. $$y=2 \csc \left(x-\frac{\pi}{3}\right)$$

Find the amplitude and period of the function, and sketch its graph. $$ y=4 \sin (-2 x) $$

Find the exact value of the trigonometric function at the given real number. $$ \begin{array}{llll}{\text { (a) } \sin \frac{25 \pi}{2}} & {\text { (b) } \cos \frac{25 \pi}{2}} & {\text { (c) } \cot \frac{25 \pi}{2}}\end{array} $$

\(21-30=\) Find the terminal point \(P(x, y)\) on the unit circle determined by the given value of \(t .\) $$ t=\frac{5 \pi}{6} $$

7–52 Find the period and graph the function. $$y=\frac{1}{2} \sec \left(x-\frac{\pi}{6}\right)$$

Find the amplitude and period of the function, and sketch its graph. $$ y=-2 \sin 2 \pi x $$

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. $$k=0.3, \quad c=0.2, \quad f=20$$

Find the amplitude and period of the function, and sketch its graph. $$ y=-3 \sin \pi x $$