91Ó°ÊÓ

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

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 21-24 and of the form \(y=k e^{-c t} \sin \omega t\) in Exercises 25-28 (b) Graph the function. $$k=15, \quad c=0.25, \quad f=0.6$$

Find the amplitude and period of the function, and sketch its graph. $$y=\cos 4 \pi x$$

Find the period, and graph the function. $$y=2 \cot 3 \pi x$$

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 21-24 and of the form \(y=k e^{-c t} \sin \omega t\) in Exercises 25-28 (b) Graph the function. $$k=100, \quad c=0.05, \quad p=4$$

Find the exact value of the expression, if it is defined. $$\sin \left(\sin ^{-1} \frac{1}{4}\right)$$

Terminal Points Find the terminal point \(P(x, y)\) on the unit circle determined by the given value of \(t\) $$t=4 \pi$$

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 CANT COPY)

Find the amplitude and period of the function, and sketch its graph. $$y=-2 \cos 3 \pi x$$

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