91Ó°ÊÓ

Find a function that models the simple harmonic motion having the given properties. Assume that the displacement is zero at time \(t=0\) amplitude 6 in., frequency \(5 / \pi \mathrm{Hz}\)

Find the missing coordinate of \(P,\) using the fact that \(P\) lies on the unit circle in the given quadrant. Coordinates $$P\left(\quad,-\frac{2}{7}\right)$$ Quadrant IV

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

Graph the function. $$g(x)=3+3 \cos x$$

Find the period and graph the function. $$y=-\cot x$$

Use a calculator to find an approximate value of each expression correct to five decimal places, if it is defined. $$\cos ^{-1}\left(-\frac{3}{7}\right)$$

Find a function that models the simple harmonic motion having the given properties. Assume that the displacement is zero at time \(t=0\) amplitude \(1.2 \mathrm{m}, \quad\) frequency \(0.5 \mathrm{Hz}\)

Find the exact value of the trigonometric function at the given real number. (a) \(\sin \left(-\frac{3 \pi}{2}\right)\) (b) \(\cos \left(-\frac{3 \pi}{2}\right)\) (c) \(\cot \left(-\frac{3 \pi}{2}\right)\)

Use a calculator to find an approximate value of each expression correct to five decimal places, if it is defined. $$\cos ^{-1}\left(\frac{4}{9}\right)$$

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