Free Printable Trig - Sum and Difference

1.

Which of the following is equivalent to $\sin\left(\alpha+\beta\right)$ ?

a)

$\sin\alpha\cos\alpha+\sin\beta\cos\beta$

b)

$\sin\alpha\cos\alpha-\sin\beta\cos\beta$

c)

$\sin\alpha\cos\beta+\cos\alpha\sin\beta$

d)

$\sin\alpha\cos\beta-\cos\alpha\sin\beta$

2.

Which of the following is equivalent to $\cos\left(\alpha-\beta\right)$ ?

a)

$\cos\alpha\cos\beta+\sin\alpha\sin\beta$

b)

$\cos\alpha\cos\beta-\sin\alpha\sin B$

c)

$\cos\alpha\sin\beta+\sin\alpha\cos\beta$

d)

$\cos\alpha\sin\beta-\sin\alpha\cos\beta$

3.

Which of the following is equivalent to $\tan\left(\alpha+\beta\right)$ ?

a)

$\frac{\tan\alpha+\tan\beta}{1-\tan\alpha\tan\beta}$

b)

$\frac{\tan\alpha-\tan\beta}{1-\tan\alpha\tan\beta}$

c)

$\frac{\tan\alpha+\tan\beta}{1+\tan\alpha\tan\beta}$

d)

$\frac{\tan\alpha-\tan\beta}{1+\tan\alpha\tan\beta}$

4.

Find the exact value of $\sin105\degree$

a)

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

b)

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

c)

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

d)

$\frac{\sqrt{3}+1}{2}$

5.

$\cos105\degree$

a)

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

b)

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

c)

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

d)

$\frac{1-\sqrt{3}}{2}$

6.

$\tan105\degree$

a)

$2-\sqrt{3}$

b)

$2+\sqrt{3}$

c)

$-2-\sqrt{3}$

d)

$-2+\sqrt{3}$

7.

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

a)

$\frac{16}{65}$

b)

$-\frac{16}{65}$

c)

$\frac{65}{16}$

d)

$-\frac{65}{16}$

8.

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

a)

$\frac{33}{65}$

b)

$-\frac{33}{65}$

c)

$\frac{63}{65}$

d)

$-\frac{63}{65}$

9.

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)

$-\frac{63}{16}$

10.

If the 2 legs of a right triangle are 7 in. and 24 in., how long is the hypotenuse?

a)

31 in.

b)

17 in.

c)

$\sqrt{527}\$ in.

d)

25 in.

Trig - Sum and Difference

Total questions: 10

Worksheet time: 50mins

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