91Ó°ÊÓ

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. $$y=2.4 \sin 3.6 t$$

Show that the point is on the unit circle. $$\left(\frac{\sqrt{11}}{6}, \frac{5}{6}\right)$$

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

Find the exact value of each expression, if it is defined. (a) \(\tan ^{-1} 0\) (b) \(\tan ^{-1}(-\sqrt{3})\) (c) \(\tan ^{-1}\left(-\frac{\sqrt{3}}{3}\right)\)

Find the exact value of the trigonometric function at the given real number. (a) \(\cos \frac{19 \pi}{6}\) (b) \(\cos \left(-\frac{7 \pi}{6}\right)\) (c) \(\cos \left(-\frac{\pi}{6}\right)\)

Find the exact value of the trigonometric function at the given real number. (a) \(\cos \frac{3 \pi}{4}\) (b) \(\cos \frac{5 \pi}{4}\) (c) \(\cos \frac{7 \pi}{4}\)

Find the period, and graph the function. $$y=3 \tan x$$

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. $$y=-0.25 \cos \left(1.5 t-\frac{\pi}{3}\right)$$

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

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