Free Printable sum and difference of angles

1.

Which of the following is the same as $\cos\ \left(A+B\right)$

a)

$\sin A\cos\ B\ +\ \cos\ A\ \sin\ B$

b)

$\sin\ A\ \cos\ B\ -\ \cos\ A\ \sin\ B$

c)

$\cos\ A\ \cos\ B\ +\ \sin\ A\ \sin\ B$

d)

$\cos\ A\ \cos\ B\ -\ \sin\ A\ \sin\ B$

2.

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)

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

3.

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}\$

4.

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

a)

$\tan75^o$

b)

$\tan\ 15^o$

c)

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

d)

$\tan90^{o\ }$

5.

Use sum or difference angles identity to find the exact value for $\sin\ \left(-15^o\right)$

a)

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

b)

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

c)

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

d)

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

6.

Given $\sin x=\frac{3}{5}and\ \sin y=\frac{2}{3},$ where $x\ and\ y$ are both in first quadrant. $Evaluate\ \sin\left(x+y\right)$

a)

$\frac{3\sqrt{5}+8}{15}$

b)

$\frac{4\sqrt{5}+6}{15}$

c)

$\frac{2\sqrt{5}+12}{15}$

d)

$\frac{4\sqrt{5}+2}{5}$

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.

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}\$

9.

Given $\sin x=\frac{3}{5}and\ \sin y=\frac{2}{3},$ where $x\ and\ y$ are both in first quadrant. $Evaluate\ \sin\left(x+y\right)$

a)

$\frac{3\sqrt{5}+8}{15}$

b)

$\frac{4\sqrt{5}+6}{15}$

c)

$\frac{2\sqrt{5}+12}{15}$

d)

$\frac{4\sqrt{5}+2}{5}$

10.

Which of the following is NOT
a solution to
sin θ = √(3) / 2 ?

a)

π / 3

b)

2π / 3

c)

5π / 3

d)

7π / 3

11.

Please choose the correct sum and difference formula:
cos (α-β) =

a)

sin α cos β + cos α sin β

b)

sin α cos β - cos α sin β

c)

cos α cos β - sin α sin β

d)

cos α cos β + sin α sin β

12.

If $\sin A=\frac{3}{5},\sin B=\frac{2}{3},$ $and\ \angle A\ and\ \angle B$ are acute angles, what is the value of $\cos\left(A-B\right)?$

a)

$-\frac{2}{3}$

b)

$\frac{4\sqrt{5}-6}{15}$

c)

$\frac{4\sqrt{5}+2}{5}$

d)

$\frac{4\sqrt{5}+6}{15}$

13.

Expand and simplify $\cos\ \left(90^o-x\right)$

a)

$\cos\ x$

b)

$\sin\ x$

c)

$\tan\ x$

d)

$-\cos x$

14.

Expand and simplify $\tan\ \left(x+\frac{\pi}{4}\right)$

a)

$\tan\ x+1$

b)

$\tan x-1$

c)

$\frac{\tan\ x+1}{1-\tan x}$

d)

$\frac{\tan x-1}{1+\tan x}$

15.

Use sum or difference angles 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)

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

sum and difference of angles

Total questions: 15

Worksheet time: 17mins

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