Free Printable Sum/Difference, Double and Half Angles Quiz (9.2 to 9.3)

1.

Simplify:

$\tan^2\left(\theta\right)\left(1-\csc^2\left(\theta\right)\right)$

a)

-1

b)

$\cos\theta$

c)

1

d)

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

2.

Simplify:

$\cos\left(x\right)\sec\left(x\right)-\cos^2\left(x\right)$

a)

$-\sin^2\left(x\right)$

b)

$-\csc\left(x\right)$

c)

$\tan\left(x\right)$

d)

$\sin^2\left(x\right)$

3.

Expand $\sin\ \left(33^{o\ }+42^o\right)$

a)

$\sin\ 75^{o\ }$

b)

$\sin\ 33^o\cos42^o+\cos33^o\sin42^o$

c)

$\sin\ 33^o\cos42^o-\cos33^o\sin42^o$

d)

$\cos33^o\cos42^o+\sin33^o\sin42^o$

4.

Expand $\cos\ \left(\frac{\pi}{5}+\frac{\pi}{6}\right)$

a)

$\cos\frac{\pi}{5}\cos\frac{\pi}{6}-\sin\frac{\pi}{5}\sin\frac{\pi}{6}\$

b)

$\cos\frac{\pi}{5}\cos\frac{\pi}{6}+\sin\frac{\pi}{5}\sin\frac{\pi}{6}\$

c)

$\cos\ \frac{2\pi}{11}$

d)

$\cos\frac{\pi}{5}\sin\frac{\pi}{6}-\cos\frac{\pi}{5}\sin\frac{\pi}{6}\$

5.

$\frac{\tan45^o+\tan30^o}{1-\tan45^o\tan30^o}$ is equivalent to

a)

$\tan75^o$

b)

$\tan\ 15^o$

c)

$\frac{\sin45^o}{\cos30^o}$

d)

$\tan90^{o\ }$

6.

Use sum or difference identity to find the exact value for $\cos105^o$

a)

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

b)

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

c)

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

d)

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

7.

Write the following expression as the sine, cosine, or tangent of an angle.
cos(175)cos(55)+sin(175)sin(55)

a)

sin(120)

b)

cos(120)

c)

cos(230)

d)

sin(230)

8.

Evaluate the expression:

$\tan\left(\frac{13\pi}{12}\right)$

a)

$2-\sqrt[]{3}$

b)

$2+\sqrt[]{3}$

c)

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

d)

$-2-\sqrt[]{3}$

9.

$\sin2\theta=$

a)

$\left(\sin\theta\right)\left(\cos\theta\right)$

b)

$2\left(\sin\theta\right)\left(\cos\theta\right)$

c)

$\sin^2\theta$

d)

$2\sin^2\theta$

10.

Find the exact value of sin 2x if $\sin\left(x\right)=\frac{12}{13}$ and x is in the first quadrant.

a)

120/169

b)

25/169

c)

60/169

d)

5/13

11.

Using the second identity, find Cos(50)

a)

sin²(25) - cos²(25)

b)

cos²(50) - sin²(50)

c)

cos²(25) - sin²(25)

d)

sin²(50) - cos²(50)

12.

Use a double-angle or half-angle identity to find the exact value of each expression
sin θ = −3/5 and 3π/2 < θ < 2π Find tan θ/2

a)

-1/3

b)

-√3

c)

√3/3

d)

-1

13.

Find the equivalent expression to:

$\cos^23x-\sin^23x$

a)

$\cos\ 6x$

b)

$\cos\ 6x^2$

c)

$\cos\ \frac{3x}{2}$

d)

$\sin\ 6x$

14.

Find the equivalent to

$\tan\frac{\pi}{3}$

a)

$\frac{2\tan\frac{\pi}{6}}{1-\tan^2\frac{\pi}{6}}$

b)

$\frac{2\tan\frac{\pi}{3}}{1-\tan^2\frac{\pi}{3}}$

c)

$\frac{2\tan\frac{2\pi}{3}}{1-\tan^2\frac{2\pi}{3}}$

d)

$\frac{2\tan\frac{\pi}{12}}{1-\tan^2\frac{\pi}{12}}$

15.

Find the exact value of

$\sin\left(-\frac{\pi}{12}\right)$

a)

$-\ \sqrt[]{\frac{1-\cos\left(\frac{\pi}{6}\right)}{2}}$

b)

$\ \sqrt[]{\frac{1-\cos\left(\frac{\pi}{6}\right)}{2}}$

c)

$-\ \sqrt[]{\frac{1-\cos\left(\frac{\pi}{12}\right)}{2}}$

d)

$-\ \sqrt[]{\frac{1-\cos\left(\frac{\pi}{3}\right)}{2}}$

Sum/Difference, Double and Half Angles Quiz (9.2 to 9.3)

Total questions: 15

Worksheet time: 30mins

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