91Ó°ÊÓ

let \(\theta\) be an angle in standard position. Name the quadrant in which \(\theta\) lies. $$ \sin \theta>0, \quad \cos \theta>0 $$

In Exercises 17–24, graph two periods of the given cotangent function. $$ y=2 \cot x $$

\(\theta\) is an acute angle and sin u and cos u are given. Use identities to find tan \(\theta\), csc \(\theta\), sec \(\theta\), and cot \(\theta\). Where necessary, rationalize denominators. $$ \sin \theta=\frac{8}{17}, \quad \cos \theta=\frac{15}{17} $$

Find the exact value of each expression. $$ \tan ^{-1}(-\sqrt{3}) $$

In Exercises \(13-20,\) convert each angle in degrees to radians. Express your answer as a multiple of \(\pi\). $$ 300^{\circ} $$

\(\theta\) is an acute angle and sin u and cos u are given. Use identities to find tan \(\theta\), csc \(\theta\), sec \(\theta\), and cot \(\theta\). Where necessary, rationalize denominators. $$ \sin \theta=\frac{3}{5}, \quad \cos \theta=\frac{4}{5} $$

let \(\theta\) be an angle in standard position. Name the quadrant in which \(\theta\) lies. $$ \sin \theta<0, \quad \cos \theta>0 $$

In Exercises 17–24, graph two periods of the given cotangent function. $$ y=\frac{1}{2} \cot x $$

Determine the amplitude, period, and phase shift of each function. Then graph one period of the function. $$y=\sin \left(x-\frac{\pi}{2}\right)$$

Find the exact value of each expression. $$ \tan ^{-1}\left(-\frac{\sqrt{3}}{3}\right) $$