91Ó°ÊÓ

Find the exact value of the trigonometric function at the given real number. $$ \text { (a) }\cos \left(-\frac{\pi}{4}\right) \quad \text { (b) } \csc \left(-\frac{\pi}{4}\right) \quad \text { (c) } \cot \left(-\frac{\pi}{4}\right) $$

\(13-18=\) The point \(P\) is on the unit circle. Find \(P(x, y)\) from the given information. The \(x\) -coordinate of \(P\) is \(-\sqrt{2} / 3\) and \(P\) lies below the \(x\) -axis.

Find the amplitude and period of the function, and sketch its graph. $$ y=\frac{1}{2} \cos 4 x $$

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

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. $$k=15, \quad c=0.25, \quad f=0.6$$

\(13-18=\) The point \(P\) is on the unit circle. Find \(P(x, y)\) from the given information. The \(x\) -coordinate of \(P\) is \(-\frac{2}{5}\) and \(P\) lies above the \(x\) -axis.

Find the exact value of the trigonometric function at the given real number. $$ \begin{array}{llll}{\text { (a) } \sin \frac{5 \pi}{4}} & {\text { (b) } \sec \frac{5 \pi}{4}} & {\text { (c) } \tan \frac{5 \pi}{4}}\end{array} $$

Find the amplitude and period of the function, and sketch its graph. $$ y=10 \sin \frac{1}{2} x $$

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. $$k=100, \quad c=0.05, \quad p=4$$

Find the exact value of the trigonometric function at the given real number. $$ \begin{array}{lll}{\text { (a) } \csc \left(-\frac{\pi}{2}\right)} & {\text { (b) } \csc \frac{\pi}{2}} & {\text { (c) } \csc \frac{3 \pi}{2}}\end{array} $$