91Ó°ÊÓ

Graph the function. $$f(x)=-2+\sin x$$

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. $$\begin{array}{lc} \text { Coordinates } & \text { Quadrant } \\ P\left(\text{___},-\frac{7}{25}\right) & \text { IV } \\ \end{array}$$

Find the exact value of each expression, if it is defined. (a) \(\cos ^{-1} 0\) (b) \(\sin ^{-1} 0\) (c) \(\sin ^{-1}\left(-\frac{1}{2}\right)\)

Graph the function. $$f(x)=-1+\cos x$$

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. $$y=-\frac{3}{2} \sin (0.2 t+1.4)$$

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) \(\cot \frac{7 \pi}{3}\)

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. $$g(x)=3 \cos x$$

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. $$y=5 \cos \left(\frac{2}{3} t+\frac{3}{4}\right)$$