Free Printable Sum/Difference and Double/Half Angle Identities Review

1.

Find the exact value

$\sin165°$

a)

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

b)

$\sqrt{3}-2$

c)

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

d)

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

2.

Find the exact value

$\cos-75°$

a)

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

b)

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

c)

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

d)

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

3.

Find the exact value

$\tan-\frac{7\pi}{12}$

a)

$\sqrt{3}-2$

b)

$2+\sqrt{3}$

c)

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

d)

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

4.

Find the exact value

$\cos\frac{\pi}{12}$

a)

$\sqrt{3}-2$

b)

$2-\sqrt{3}$

c)

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

d)

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

5.

Find the exact value

$\frac{\tan178+\tan2}{1-\tan178\tan2}$

a)

$0$

b)

$undefined$

c)

$\frac{\sqrt{3}}{2}$

d)

$\frac{1}{2}$

6.

Find the exact value

$\sin55\cos10-\cos55\sin10$

a)

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

b)

$\frac{1}{2}$

c)

$\frac{\sqrt{3}}{2}$

d)

$1$

7.

Simplify

$\cos\left(270+\theta\right)$

a)

$\sin\theta$

b)

$-\sin\theta$

c)

$\cos\theta$

d)

$-\cos\theta$

8.

Simplify

$\cos\left(\theta-90\right)$

a)

$\sin\theta$

b)

$-\sin\theta$

c)

$\cos\theta$

d)

$-\cos\theta$

9.

$Given\ \sin\theta=-\frac{4}{\ 5\ }in\ Q3,\ find\ \tan2\theta.$

a)

$\frac{24}{7}$

b)

$-\frac{24}{7}$

c)

$-\frac{24}{25}$

d)

$\frac{24}{25}$

10.

$Given\ \cos\theta=-\frac{\sqrt{17}}{17}in\ Q4,\ find\ \cos2\theta.$

a)

$\frac{8}{15}$

b)

$-\frac{15}{17}$

c)

$\frac{8}{17}$

d)

$-\frac{15}{8}$

11.

$Given\ \tan\theta=-\frac{15}{8}\ in\ Q2,\ find\ \tan2\theta.$

a)

$-\frac{161}{240}$

b)

$\frac{240}{161}$

c)

$-\frac{240}{161}$

d)

$\frac{240}{289}$

12.

$Given\ \cos\theta=-\frac{5}{13}\ in\ Q3,\ find\ \sin\frac{\theta}{2}.$

a)

$\frac{3\sqrt{13}}{13}$

b)

$\frac{\sqrt{13}}{2}$

c)

$-\frac{\sqrt{13}}{3}$

d)

$-\frac{2}{3}$

13.

$Given\ \sin\theta=-\frac{15}{17}\ in\ Q3,\ find\ \cos\frac{\theta}{2}.$

a)

$\frac{\sqrt{34}}{5}$

b)

$-\frac{5}{3}$

c)

$-\frac{3\sqrt{34}}{34}$

d)

$\frac{5\sqrt{34}}{34}$

14.

$Given\ \tan\theta=-\frac{4}{3}\ in\ Q2,\ find\ \tan\frac{\theta}{2}.$

a)

$\sqrt{5}$

b)

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

c)

$2$

d)

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

15.

Use the half-angle identities to find the exact value of $\cos105°$

a)

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

b)

$-2-\sqrt{3}$

c)

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

d)

$\frac{\sqrt{2+\sqrt{2}}}{2}$

16.

Use the half-angle identities to find the exact value of $\tan67.5°$

a)

$1+\sqrt{2}$

b)

$\sqrt{2}-1$

c)

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

d)

$\frac{\sqrt{2+\sqrt{2}}}{2}$

17.

$Given\ \tan\theta=\frac{5}{12}\ in\ Q3,\ find\ \sin2\theta.$

a)

$\frac{120}{169}$

b)

$-\frac{120}{169}$

c)

$\frac{119}{169}$

d)

$\frac{120}{119}$

Sum/Difference and Double/Half Angle Identities Review

Total questions: 17

Worksheet time: 3hrs 50mins

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