91Ó°ÊÓ

23-32 \(\approx\) Find the terminal point \(P(X, y)\) on the unit circle determined by the given value of \(t\) $$ t=\frac{2 \pi}{3} $$

Find the period and graph the function. $$ y=\tan \frac{\pi}{4} x $$

\(29-42\) . Find the amplitude, period, and phase shift of the function, and graph one complete period. $$ y=\cos \left(x-\frac{\pi}{2}\right) $$

The terminal point \(P(x, y)\) determined by a real number \(t\) is given. Find \(\sin t, \cos t,\) and \(\tan t\). \(\left(\frac{3}{5}, \frac{4}{5}\right)\)

\(23-44=\) Find the exact value of the expression, if it is defined. \(\cos ^{-1}\left(\cos \frac{5 \pi}{6}\right)\)

The terminal point \(P(x, y)\) determined by a real number \(t\) is given. Find \(\sin t, \cos t,\) and \(\tan t\). \(\left(-\frac{3}{5}, \frac{4}{5}\right)\)

Predator Population Model In a predator/prey model the predator population is modeled by the function $$ y=900 \cos 2 t+8000 $$ where \(t\) is measured in years. (a) What is the maximum population? (b) Find the length of time between successive periods of maximum population.

\(23-44=\) Find the exact value of the expression, if it is defined. \(\tan ^{-1}\left(\tan \left(\frac{\pi}{4}\right)\right)\)

23-32 \(\approx\) Find the terminal point \(P(X, y)\) on the unit circle determined by the given value of \(t\) $$ t=-\frac{\pi}{2} $$

Find the period and graph the function. $$ y=\cot \frac{\pi}{2} x $$