91Ó°ÊÓ

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

Find the exact value of the trigonometric function at the given real number. (a) \(\sin \frac{25 \pi}{2}\) (b) \(\cos \frac{25 \pi}{2}\) (c) \(\cot \frac{25 \pi}{2}\)

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

Find the exact value of the expression, if it is defined. $$\cos \left(\cos ^{-1} \frac{2}{3}\right)$$

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

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

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

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 \(19-22,\) and of the form \(y=k e^{-c t}\) sin \(\omega t\) in Exercises \(23-26\) (b) Graph the function. $$k=0.3, \quad c=0.2, \quad f=20$$

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. $$t=0$$ (TABLE CAN'T COPY).

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