91Ó°ÊÓ

Find the reference angle \(\theta^{\prime}\) for the special angle \(\theta .\) Sketch \(\theta\) in standard position and label \(\boldsymbol{\theta}^{\prime}\). $$\theta=315^{\circ}$$

Use the function value(s) and the trigonometric identities to evaluate each trigonometric function. \(\sin 30^{\circ}=\frac{1}{2}, \tan 30^{\circ}=\frac{\sqrt{3}}{3}\) (a) \(\csc 30^{\circ}\) (b) \(\cot 60^{\circ}\) (c) \(\cos 30^{\circ}\) (d) \(\cot 30^{\circ}\)

Use the properties of inverse functions to find the exact value of the expression, if possible. tan(arctan 25)

Sketch the graph of the function. Use a graphing utility to verify your sketch. (Include two full periods.) $$y=2 \cos x-3$$

Determine the quadrant in which each angle lies. (The angle measure is given in radians.) (a) \(-\frac{5 \pi}{12}\) (b) \(-\frac{13 \pi}{9}\)

Determine the quadrant in which each angle lies. (The angle measure is given in radians.) (a) \(-1\) (b) \(-2\)

Find the reference angle \(\theta^{\prime}\) for the special angle \(\theta .\) Sketch \(\theta\) in standard position and label \(\boldsymbol{\theta}^{\prime}\). $$\theta=-45^{\circ}$$

Use the function value(s) and the trigonometric identities to evaluate each trigonometric function. \(\csc \theta=3, \sec \theta=\frac{3 \sqrt{2}}{4}\) (a) \(\sin \theta\) (b) \(\cos \theta\) (c) \(\tan \theta\) (d) \(\sec \left(90^{\circ}-\theta\right)\)

Sketch the graph of the function. Use a graphing utility to verify your sketch. (Include two full periods.) $$y=\frac{2}{3} \cos \left(\frac{x}{2}-\frac{\pi}{4}\right)$$

Harmonic Motion Find a model for simple harmonic motion satisfying the specified conditions. Displacement \((t=0)$$\quad\)Amplitude\(\quad\)Period 0\(\quad\)8 centimeters\(\quad\)2 seconds