Free Printable Half-Angle Identities

1.

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

a)

$\frac{\sqrt{6}-\sqrt{2}}{4}$

b)

$-2-\sqrt{3}$

c)

$\frac{\sqrt{2-\sqrt{2}}}{2}$

d)

$-\frac{\sqrt{3}}{3}$

2.

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

a)

$-\sqrt{3+2\sqrt{2}}$

b)

$\frac{\sqrt{2-\sqrt{2}}}{2}$

c)

$-2$

d)

$\frac{\sqrt{3}}{3}$

3.

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

a)

$-\frac{\sqrt{3}}{3}$

b)

$-\sqrt{3}$

c)

$\sqrt{4-2\sqrt{2}}$

d)

$-2+\sqrt{3}$

4.

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

a)

$0$

b)

$\sqrt{6}+\sqrt{2}$

c)

$\sqrt{4+2\sqrt{2}}$

d)

$1$

5.

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

a)

$\sqrt{26}$

b)

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

c)

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

d)

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

6.

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

a)

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

b)

$\frac{\sqrt{10-2\sqrt{5}}}{2}$

c)

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

d)

$\frac{\sqrt{5}}{5}$

7.

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

a)

$\frac{1}{5}$

b)

$\frac{1}{3}$

c)

$-5$

d)

$-\frac{1}{3}$

8.

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

a)

$-\sqrt{26}-5$

b)

$\frac{1}{3}$

c)

$3$

d)

$-\sqrt{26}+5$

Half-Angle Identities

Total questions: 8

Worksheet time: 2hrs 0mins

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