91Ó°ÊÓ

Evaluate the trigonometric function of the quadrant angle. $$ \cot \pi $$

Determine the quadrant in which each angle lies. (a) \(8.3^{\circ}\) (b) \(257^{\circ} 30^{\prime}\)

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

Use a graphing utility to graph the function. Include two full periods. $$ y=\sec \pi x $$

Use the value of the trigonometric function to evaluate the indicated functions. \(\sin t=\frac{1}{2}\) (a) \(\sin (-t)\) (b) \(\csc (-t)\)

Evaluate the trigonometric function of the quadrant angle. $$ \csc \pi $$

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

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 \(\left.m_{1} m_{2} \neq-1 .\right)\) $$ \begin{array}{l} L_{1}: 3 x-2 y=5 \\ L_{2}: x+y=1 \end{array} $$

Determine the quadrant in which each angle lies. (a) \(-132^{\circ} 50^{\prime}\) (b) \(-336^{\circ}\)

Use trigonometric identities to transform the left side of the equation into the right side \((0<\theta<\pi / 2)\). $$ (\sec \theta+\tan \theta)(\sec \theta-\tan \theta)=1 $$