91Ó°ÊÓ

Sketch the graph of the function. (Include two full periods.) $$ y=\cos \frac{x}{2} $$

Determine the quadrant in which each angle lies. (a) \(-260^{\circ}\) (b) \(-3.4^{\circ}\)

Sketch the graph of the function. (Include two full periods.) $$ y=\sin 4 x $$

Find the angle \(\alpha\) between two nonvertical lines \(L_{1}\) and \(L_{2}\). The angle \(\alpha\) satisfies the equation $$\tan \boldsymbol{\alpha}=\left|\frac{m_{2}-m_{1}}{1+m_{2} m_{1}}\right|$$ where \(m_{1}\) and \(m_{2}\) are the slopes of \(L_{1}\) and \(L_{2}\), respectively. (Assume that \(\left.m_{1} m_{2} \neq-1 .\right)\) $$ \begin{array}{l} L_{1}: 2 x-y=8 \\ L_{2}: \quad x-5 y=-4 \end{array} $$

Use a graphing utility to graph the function. Include two full periods. $$ y=\frac{1}{4} \cot \left(x-\frac{\pi}{2}\right) $$

Evaluate the trigonometric function of the quadrant angle. $$ \cot \frac{\pi}{2} $$

Use trigonometric identities to transform the left side of the equation into the right side \((0<\theta<\pi / 2)\). $$ \sin ^{2} \theta-\cos ^{2} \theta=2 \sin ^{2} \theta-1 $$

Use the value of the trigonometric function to evaluate the indicated functions. \(\cos (-t)=-\frac{1}{5}\) (a) \(\cos t\) (b) \(\sec (-t)\)

Sketch the graph of the function. (Include two full periods.) $$ y=\cos 2 \pi x $$

Find the reference angle \(\boldsymbol{\theta}^{\prime}\), and sketch \(\boldsymbol{\theta}\) and \(\boldsymbol{\theta}^{\prime}\) in standard position. $$ \theta=160^{\circ} $$