91Ó°ÊÓ

Find exact expressions for the indicated quantities, given that $$ \cos \frac{\pi}{12}=\frac{\sqrt{2+\sqrt{3}}}{2} \text { and } \sin \frac{\pi}{8}=\frac{\sqrt{2-\sqrt{2}}}{2} $$ [These values for \(\cos \frac{\pi}{12}\) and \(\sin \frac{\pi}{8}\) will be derived.] $$ \tan \frac{\pi}{12} $$

For Exercises \(7-14,\) sketch the unit circle and the radius corresponding to the given angle. Include an arrow to show the direction in which the angle is measured from the positive horizontal axis. $$ 460^{\circ} $$

Suppose \(\frac{\pi}{2}<\theta<\pi\) and \(\sin \theta=\frac{2}{3}\). Evaluate: (a) \(\cos \theta\) (b) \(\tan \theta\)

Find the smallest number \(\theta\) larger than \(4 \pi\) such that \(\cos \theta=0\)

Find the smallest number \(\theta\) larger than \(6 \pi\) such that \(\sin \theta=\frac{\sqrt{2}}{2}\)

In Exercises 9-16, convert each angle to degrees. $$ \frac{\pi}{10} \text { radians } $$

Find exact expressions for the indicated quantities, given that $$ \cos \frac{\pi}{12}=\frac{\sqrt{2+\sqrt{3}}}{2} \text { and } \sin \frac{\pi}{8}=\frac{\sqrt{2-\sqrt{2}}}{2} $$ [These values for \(\cos \frac{\pi}{12}\) and \(\sin \frac{\pi}{8}\) will be derived.] $$ \tan \frac{\pi}{8} $$

Suppose \(\frac{\pi}{2}<\theta<\pi\) and \(\sin \theta=\frac{3}{4} .\) Evaluate: (a) \(\cos \theta\) (b) \(\tan \theta\)

For Exercises \(7-14,\) sketch the unit circle and the radius corresponding to the given angle. Include an arrow to show the direction in which the angle is measured from the positive horizontal axis. $$ -10^{\circ} $$

Find the four smallest positive numbers \(\theta\) such that \(\cos \theta=0\)