Free Printable Addition, Subtraction, and Multiple Angle Identities Funtime

1.

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)

2.

Using the first identity, find Sin(180)

a)

2sin(90)cos(90)

b)

2sin(180)cos(180)

c)

sin(90)cos(90)

d)

sin(180)cos(180)

3.

Using the third identity, find Cos(40)

a)

2cos² (40) - 1

b)

2cos² (20) - 1

c)

2cos² (20) + 1

d)

2cos² (40) + 1

4.

Using the first identity, find Sin(180)

a)

2sin(90)cos(90)

b)

2sin(180)cos(180)

c)

sin(90)cos(90)

d)

sin(180)cos(180)

5.

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

cos θ = 4/5 and 270° < θ < 360°Find sin 2θ

a)

-1/5

b)

24/25

c)

-24/25

d)

-25/24

6.

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

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)

-1/5

b)

24/25

c)

-24/25

d)

-25/24

8.

Use a double-angle or half-angle identity to find the exact value of each expression
cos θ = 4/5 and 270° < θ < 360°Find sin 2θ

a)

-1/5

b)

24/25

c)

-24/25

d)

-25/24

9.

Find the exact value of cos $75\degree$

a)

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

b)

$\frac{\sqrt{5}+\sqrt{3}}{4}$

c)

$\frac{1}{2}$

d)

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

10.

Given angle A and B in Quadrant I with $\sin A\ =\frac{12}{13}\ and\ \cos B\ =\frac{3}{5}\ find\ \cos\left(A+B\right)$

a)

$-\frac{33}{65}$

b)

$\frac{33}{65}$

c)

$\frac{1}{2}$

d)

$\frac{12}{13}$

11.

$\sin A=\ \frac{12}{13\ }\ and\ \cos B=\ \frac{4}{5},\ find\ \cos\left(A+B\right)$ Given angle A and B in Quadrant I with

a)

$\frac{16}{45}$

b)

$\frac{16}{65}$

c)

$\frac{36}{65}$

d)

$\frac{20}{45}$

12.

$Find\ the\ exact\ value\ of\ \tan\ \frac{\pi}{12}$

a)

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

b)

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

c)

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

d)

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

13.

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)

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

14.

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)

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

15.

If the terminal side of an angle $\theta$ is located in QI, then $\cos\left(2\theta\right)$ will be:

a)

Positive

b)

Negative

c)

Positive or negative

d)

Undefined

16.

To find an exact value for the expression: $\sin\left(67.5\degree\right)$ , you should use

a)

The double angle formula

b)

The half angle formula

c)

A sum/difference formula

d)

Just put it in your calculator because it gives you exact answers.

17.

In the expression: $\frac{3-\sin x}{3+\cos x}$
the 3s can be cancelled from the numerator and denominator.

a)

True

b)

False

18.

The terminal side of an angle $\alpha$ is located in Quadrant III.

If $0\degree<\alpha<360\degree$

then $\cos\left(\frac{\alpha}{2}\right)$ must be:

a)

Positive

b)

Negative

c)

Can't tell

d)

Could be positive or negative

19.

Write as a single trig function of a single angle.
$2\sin\frac{\pi}{5}\cos\frac{\pi}{5}$

a)

$\sin\frac{\pi}{10}$

b)

$\sin\frac{2\pi}{5}$

c)

$\cos\frac{2\pi}{5}$

d)

$\cos\frac{\pi}{10}$

20.

Write as a single trig function of a single angle:
$\cos^232\degree-\sin^232\degree$

a)

$\cos64\degree$

b)

$\cos16\degree$

c)

$\sin64\degree$

d)

$\sin16\degree$

21.

Write as a single trig function of a single angle:
$\frac{2\tan140\degree}{1-\tan^2140\degree}$

a)

$\tan140\degree$

b)

$\tan70\degree$

c)

$\tan280\degree$

d)

$\cot280\degree$

22.

Use a double angle identity to find the exact value of
$\cos450\degree$

a)

$-1$

b)

0

c)

$\frac{1}{2}$

d)

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

23.

$\sin x=\frac{12}{13}\ \ and\ \ \frac{\pi}{2}<x<\pi$

Find the exact value of $\tan2x$ .

a)

$-\frac{120}{119}$

b)

$\frac{119}{169}$

c)

$-\frac{119}{169}$

d)

$\frac{120}{119}$

24.

The terminal side of an angle $\beta$ is located in Quadrant IV and
$0\degree<\beta<360\degree$
$\tan\left(\frac{\beta}{2}\right)$ must be:

a)

Positive

b)

Negative

c)

Can't tell

d)

Could be positive or negative

Addition, Subtraction, and Multiple Angle Identities Funtime

Total questions: 24

Worksheet time: 2hrs 53mins

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