91Ó°ÊÓ

Points on the Unit Circle Find the missing coordinate of \(P,\) using the fact that \(P\) lies on the unit circle in the given quadrant. $$\begin{array}{lc} \text { Coordinates } & \text { Quadrant } \\ P\left(\text{___}, \frac{1}{3}\right) & \text { II } \end{array}$$

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

The given function models the displacement of an object moving in simple harmonic motion. (a) Find the amplitude, period, and frequency of the motion. (b) Sketch a graph of the displacement of the object over one complete period. $$y=1.6 \sin (t-1.8)$$

Graph the function. $$g(x)=2 \sin x$$

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

Points on the Unit Circle Find the missing coordinate of \(P,\) using the fact that \(P\) lies on the unit circle in the given quadrant. $$\begin{array}{lc} \text { Coordinates } & \text { Quadrant } \\ \hline P\left(\frac{2}{5},\right.\text{___}) & \text { I } \end{array}$$

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

Find the period, and graph the function. $$y=\frac{3}{4} \tan x$$

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 cm, period 3 s

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