Half-Angle Identities

Use a half-angle identity to find the exact value of  $\sin165\degree$  

•  $\frac{\sqrt{6}-\sqrt{2}}{4}$  

•  $-2-\sqrt{3}$  

•  $\frac{\sqrt{2-\sqrt{2}}}{2}$  

•  $-\frac{\sqrt{3}}{3}$  

Use a half-angle identity to find the exact value of  $\tan\left(\frac{5\pi}{8}\right)$  

•  $-\sqrt{3+2\sqrt{2}}$  

•  $\frac{\sqrt{2-\sqrt{2}}}{2}$  

•  $-2$  

•  $\frac{\sqrt{3}}{3}$  

Use a half-angle identity to find the exact value of  $\cot\left(\frac{7\pi}{12}\right)$  

•  $-\frac{\sqrt{3}}{3}$  

•  $-\sqrt{3}$  

•  $\sqrt{4-2\sqrt{2}}$  

•  $-2+\sqrt{3}$  

Use a half-angle identity to find the exact value of  $\sec67.5\degree$  

•  $0$  

•  $\sqrt{6}+\sqrt{2}$  

•  $\sqrt{4+2\sqrt{2}}$  

•  $1$  

 $\tan\theta=-\sqrt{14}$ and  $\frac{\pi}{2}<\theta<\pi$ find  $\cos\left(\frac{\theta}{2}\right)$  

•  $\sqrt{26}$  

•  $\frac{\sqrt{58+10\sqrt{29}}}{2}$  

•  $\frac{\sqrt{450-30\sqrt{15}}}{30}$  

•  $\frac{\sqrt{105-7\sqrt{15}}}{7}$  

 $\tan\theta=-2$ and  $90\degree<\theta<180\degree$ find  $\csc\left(\frac{\theta}{2}\right)$  

•  $\frac{\sqrt{50+10\sqrt{5}}}{10}$  

•  $\frac{\sqrt{10-2\sqrt{5}}}{2}$  

•  $\frac{\sqrt{50-10\sqrt{5}}}{10}$  

•  $\frac{\sqrt{5}}{5}$  

 $\cot\theta=\frac{12}{5}$ and  $180\degree<\theta<270\degree$ find  $\tan\left(\frac{\theta}{2}\right)$  

•  $\frac{1}{5}$  

•  $\frac{1}{3}$  

•  $-5$  

•  $-\frac{1}{3}$  

 $\csc\theta=-\sqrt{26}$ and  $270\degree<\theta<360\degree$ find  $\tan\left(\frac{\theta}{2}\right)$  

•  $-\sqrt{26}-5$  

•  $\frac{1}{3}$  

•  $3$  

•  $-\sqrt{26}+5$