91Ó°ÊÓ

Use the properties of inverse functions to find the exact value of the expression, if possible. \(\tan \left[\tan ^{-1}(-0.5)\right]\)

Harmonic Motion Find a model for simple harmonic motion satisfying the specified conditions. Displacement \((t=0)$$\quad\)Amplitude\(\quad\)Period 3 inches\(\quad\)3 inches\(\quad\)1.5 seconds

Sketch each angle in standard position. (a) \(\frac{3 \pi}{4}\) (b) \(\frac{4 \pi}{3}\)

Use the properties of inverse functions to find the exact value of the expression, if possible. cos[cos \(\left.^{1}(-2)\right]\)

Find the reference angle \(\theta^{\prime}\) for the special angle \(\theta .\) Sketch \(\theta\) in standard position and label \(\boldsymbol{\theta}^{\prime}\). $$\theta=\frac{3 \pi}{4}$$

Use a graphing utility to graph the function. (Include two full periods.) Identify the amplitude and period of the graph. $$y=-10 \cos \frac{\pi x}{6}$$

Use the function value(s) and the trigonometric identities to evaluate each trigonometric function. \(\tan \beta=3\) (a) \(\cot \beta\) (b) \(\cos \beta\) (c) \(\tan \left(90^{\circ}-\beta\right)\) (d) \(\csc \beta\)

Harmonic Motion Find a model for simple harmonic motion satisfying the specified conditions. Displacement \((t=0)$$\quad\)Amplitude\(\quad\)Period -2 feet\(\quad\)2 feet\(\quad\)10 seconds

Use the properties of inverse functions to find the exact value of the expression, if possible. \(\arctan \left(\tan \frac{11 \pi}{6}\right)\)

Sketch each angle in standard position. (a) \(-\frac{7 \pi}{4}\) (b) \(-\frac{5 \pi}{2}\)