91Ó°ÊÓ

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

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

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

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

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

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 missing coordinate of \(P,\) using the fact that \(P\) lies on the unit circle in the given quadrant. Coordinates $$P\left(-\frac{3}{5}, \quad\right)$$ Quadrant III

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) \(\tan ^{-1} 1\)

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

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) \(\cos \frac{7 \pi}{4}\)