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 in Examples 4 and 5 in Section 6.3.] $$ \tan \left(-\frac{\pi}{8}\right) $$

Convert each angle to degrees. 5 radians

Find the lengths of both circular arcs on the unit circle connecting the points (1,0) and \(\left(-\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)\)

Evaluate \(\sin \left(\cos ^{-1} \frac{1}{3}\right)\)

Given that \(\cos 15^{\circ}=\frac{\sqrt{2+\sqrt{3}}}{2}\) and \(\sin 22.5^{\circ}=\frac{\sqrt{2-\sqrt{2}}}{2}\). Find exact expressions for the indicated quantities. $$ \tan 15^{\circ} $$

Convert each angle to degrees. \(-\frac{2 \pi}{3}\) 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 in Examples 4 and 5 in Section 6.3.] $$ \cos \frac{25 \pi}{12} $$

Given that \(\cos 15^{\circ}=\frac{\sqrt{2+\sqrt{3}}}{2}\) and \(\sin 22.5^{\circ}=\frac{\sqrt{2-\sqrt{2}}}{2}\). Find exact expressions for the indicated quantities. $$ \tan 22.5^{\circ} $$

Convert each angle to degrees. \(-\frac{3 \pi}{4}\) 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 in Examples 4 and 5 in Section 6.3.] $$ \cos \frac{17 \pi}{8} $$