91Ó°ÊÓ

23-32 \(\approx\) Find the terminal point \(P(X, y)\) on the unit circle determined by the given value of \(t\) $$ t=\frac{5 \pi}{6} $$

\(23-44=\) Find the exact value of the expression, if it is defined. \(\tan \left(\tan ^{-1} 5\right)\)

\(23-44=\) Find the exact value of the expression, if it is defined. \(\sin \left(\sin ^{-1} 5\right)\)

23-32 \(\approx\) Find the terminal point \(P(X, y)\) on the unit circle determined by the given value of \(t\) $$ t=\frac{7 \pi}{6} $$

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

\(17-28\) . Find the amplitude and period of the function, and sketch its graph. $$ y=-3 \sin \pi x $$

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 \(19-22,\) and of the form \(y=k e^{-c t} \sin \omega t\) in Exercises \(23-26\) (b) Graph the function. $$ k=12, \quad c=0.01, \quad f=8 $$

Find the value of each of the six trigonometric functions (if it is defined) at the given real number \(t\). Use your answers to complete the table. \(t=\frac{\pi}{2}\)

Find the period and graph the function. $$ y=\tan 4 x $$

23-32 \(\approx\) Find the terminal point \(P(X, y)\) on the unit circle determined by the given value of \(t\) $$ t=-\frac{\pi}{3} $$