91Ó°ÊÓ

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. $$ k=2, \quad c=1.5, \quad f=3 $$

15-20 \(\mathbf{m}\) 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.

\(17-28\) . Find the amplitude and period of the function, and sketch its graph. $$ y=\frac{1}{2} \cos 4 x $$

15-20 \(\mathbf{m}\) 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 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 \(19-22,\) and of the form \(y=k e^{-c t} \sin \omega t\) in Exercises \(23-26\) (b) Graph the function. $$ k=15, \quad c=0.25, \quad f=0.6 $$

Find the exact value of the trigonometric function at the given real number. (a) \(\sin \frac{5 \pi}{4} \quad\) (b) \(\sec \frac{5 \pi}{4} \quad\) (c) \(\tan \frac{5 \pi}{4}\)

\(17-28\) . Find the amplitude and period of the function, and sketch its graph. $$ y=10 \sin \frac{1}{2} x $$

Find the exact value of the trigonometric function at the given real number. (a) \(\sin \frac{5 \pi}{4} \quad\) (b) \(\csc \frac{\pi}{2} \quad\) (c) \(\csc \frac{3 \pi}{2}\)

\(11-22\) . Use a calculator to find an approximate value of each expression correct to five decimal places, if it is defined. \(\sin ^{-1}(-0.25713)\)