91Ó°ÊÓ

\(11-14\) a Find a function that models the simple harmonic motion having the given properties. Assume that the displacement is zero at time \(t=0\) amplitude \(10 \mathrm{cm}, \quad\) period \(3 \mathrm{s}\)

Find the exact value of the trigonometric function at the given real number. (a) \(\sin \frac{7 \pi}{3}\) (b) \(\csc \frac{7 \pi}{3}\) (c) \(\cot \frac{7 \pi}{3}\)

Use a calculator to find an approximate value of each expression correct to five decimal places, if it is defined. $$\sin ^{-1} \frac{2}{3}$$

Graph the function. $$g(x)=-\frac{1}{2} \sin x$$

Graph the function. $$g(x)=-\frac{2}{3} \cos x$$

Find the exact value of the trigonometric function at the given real number. (a) \(\cos \left(-\frac{\pi}{3}\right)\) (b) \(\sec \left(-\frac{\pi}{3}\right)\) (c) \(\tan \left(-\frac{\pi}{3}\right)\)

Find a function that models the simple harmonic motion having the given properties. Assume that the displacement is zero at time \(t=0\) amplitude \(24 \mathrm{ft},\) period \(2 \mathrm{min}\)

Use a calculator to find an approximate value of each expression correct to five decimal places, if it is defined. $$\sin ^{-1}\left(-\frac{8}{9}\right)$$

Find the missing coordinate of \(P,\) using the fact that \(P\) lies on the unit circle in the given quadrant. Coordinates $$P\left(\frac{2}{5}, \quad\right)$$ Quadrant I

Find the period and graph the function. $$y=\frac{1}{2} \tan x$$