Free Printable Trig - Sum and Difference of Angles

1.

If $\sin A=\frac{3}{5},\sin B=\frac{2}{3},$ $and\ \angle A\ and\ \angle B$ are in the first quadrant, 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)

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

2.

If A and B are first quadrant angles with sinA=15/17 and cosB=4/5, find cos(A - B).

a)

3/8

b)

8/17

c)

-13/85

d)

77/85

3.

(sinu)(cosv) + (cosu)(sinv) =

a)

cos(u - v)

b)

cos(u + v)

c)

sin(u - v)

d)

sin(u + v)

4.

(sinu)(cosv) - (cosu)(sinv) =

a)

cos(u - v)

b)

cos(u + v)

c)

sin(u - v)

d)

sin(u + v)

5.

Write the expression as the sine or cosine of a single angle:

$\sin\left(\frac{\pi}{3}\right)\cos\left(\frac{\pi}{7}\right)-\sin\left(\frac{\pi}{7}\right)\cos\left(\frac{\pi}{3}\right)$

a)

$\cos\left(\frac{4\pi}{21}\right)$

b)

$\sin\left(\frac{4\pi}{21}\right)$

c)

$\cos\left(\frac{10\pi}{21}\right)$

d)

$\sin\left(\frac{10\pi}{21}\right)$

6.

Write the expression as the sine or cosine of a single angle:

$\cos\left(\frac{\pi}{7}\right)\cos x+\sin\left(\frac{\pi}{7}\right)\sin x$

a)

$\cos\left(\frac{\pi}{7}-x\right)$

b)

$\sin\left(\frac{\pi}{7}-x\right)$

c)

$\cos\left(\frac{\pi}{7}+x\right)$

d)

$\sin\left(\frac{\pi}{7}+x\right)$

7.

Write the expression as the sine or cosine of a single angle:

$\cos\left(7y\right)\cos\left(3y\right)-\sin\left(7y\right)\sin\left(3y\right)$

a)

$\cos\left(4y\right)$

b)

$\sin\left(4y\right)$

c)

$\cos\left(10y\right)$

d)

$\sin\left(10y\right)$

8.

$\cos70^o\cos40^o-\sin70^o\sin40^o\$ is equivalent to

a)

$\cos30^o$

b)

$\cos70^{o\ }$

c)

$\cos110^o$

d)

$\sin70^{o\ }$

9.

If $\tan A=\frac{2}{3}\ and\ \tan B=\frac{1}{2},$ what is the value of $\tan\left(A+B\right)?$

a)

$\frac{1}{8}$

b)

$\frac{7}{8}$

c)

$\frac{1}{4}$

d)

$\frac{7}{4}$

10.

If $\sin A=\frac{4}{5},\tan B=\frac{5}{12},$ and A and B are first quadrant angles, what is the value of $\sin\left(A+B\right)$ ?

a)

$\frac{63}{65}$

b)

$-\frac{33}{65}$

c)

$\frac{33}{65}$

d)

$-\frac{63}{65}$

11.

$\tan105\degree$

a)

$2-\sqrt{3}$

b)

$2+\sqrt{3}$

c)

$-2-\sqrt{3}$

d)

$-2+\sqrt{3}$

12.

If $\sin\alpha=\frac{5}{13}$ and $\cos\beta=\frac{4}{5}$ (both in QI), find $\tan\left(\alpha-\beta\right)$

a)

$\frac{16}{63}$

b)

$-\frac{16}{63}$

c)

$\frac{63}{16}$

d)

$-\frac{63}{16}$

Trig - Sum and Difference of Angles

Total questions: 12

Worksheet time: 3hrs 0mins

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