Free Printable Sum/Difference & Double Angle Formulas

1.

Find the exact value of the expression.
$\sin\left(\frac{5\pi}{12}\right)\cos\left(\frac{\pi}{4}\right)-\cos\left(\frac{5\pi}{12}\right)\sin\left(\frac{\pi}{4}\right)$

a)

$\frac{1}{2}$

b)

$-\frac{1}{2}$

c)

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

d)

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

2.

Given $\sin\alpha=-\frac{3}{5},\ \cos\alpha=-\frac{4}{5}$ and $\cos\beta=\frac{2\sqrt{5}}{5},\ \sin\beta=-\frac{\sqrt{5}}{5}$
Find the exact value of sin (α+β):

a)

0

b)

$-\frac{2\sqrt{5}}{25}$

c)

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

d)

$\frac{\sqrt{8}}{4}$

3.

Given tan α = 3/4 and tan β = (-1/2)

Please find the sum and difference:

tan (α-β)=

a)

$-\frac{10\sqrt{5}}{25}$

b)

$-\frac{2\sqrt{5}}{25}$

c)

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

d)

2

4.

Find the exact value.
$\cos\left(265\degree-25\degree\right)$

a)

$\frac{53}{12}$

b)

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

c)

$-\frac{1}{2}$

d)

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

5.

Use a sum or difference formula to find an exact value of sin 105º

a)

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

b)

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

c)

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

d)

$2-\sqrt{3}$

6.

Please select the correct solution

cos²x + sin ²x=

^{(It's on your reference sheet!!)}

a)

1

b)

csc²x + sec²x

c)

sin²x

d)

1 - sin²x

7.

Use a double-angle identity to find the exact value of each expression

cos θ = 4/5 and 270° < θ < 360°

Find sin 2θ

a)

$-\frac{1}{5}$

b)

$\frac{24}{25}$

c)

$-\frac{24}{25}$

d)

$-\frac{25}{24}$

8.

Find the exact value of $\sin2x$ if $\sin x=\frac{12}{13}$ and x is in the first quadrant.

a)

$\frac{120}{169}$

b)

$\frac{25}{169}$

c)

$\frac{60}{169}$

d)

$\frac{5}{13}$

9.

sin2u =

a)

$\sin u\cos u$

b)

$2\sin u\cos u$

c)

$\sin^2u$

d)

$2\sin^2u$

10.

If $\sin\theta=\frac{\sqrt{5}}{3}$ , then $\cos2\theta$ equals

a)

$\frac{1}{3}$

b)

$-\frac{1}{3}$

c)

$\frac{1}{9}$

d)

$-\frac{1}{9}$

Sum/Difference & Double Angle Formulas

Total questions: 10

Worksheet time: 30mins

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