Free Printable Sum and Difference, Double Angle, Inverse Trig Quiz

1.

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

a)

$\frac{16}{45}$

b)

$\frac{16}{65}$

c)

$\frac{36}{65}$

d)

$\frac{20}{45}$

2.

Find the exact value of sin $75\degree$

a)

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

b)

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

c)

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

d)

$\frac{\sqrt{7}}{4}$

3.

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)

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

4.

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)

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

5.

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

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.

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

a)

$\frac{1}{3}$

b)

$-\frac{1}{3}$

c)

$\frac{1}{9}$

d)

$-\frac{1}{9}$

10.

sin^-1(-1/2)

a)

π/3

b)

π/6

c)

5π/6

d)

-π/6

11.

sec^-1(-2)

a)

π/3

b)

2π/3

c)

π/6

d)

5π/6

12.

tan^-1(√(3))

a)

π/3

b)

2π/3

c)

π/6

d)

5π/6

13.

Solve equation for $0\le\theta<2\pi$ .
$-2+\cot\theta=-3$

a)

$\theta=\frac{3\pi}{4},\frac{4\pi}{3},\frac{7\pi}{4}$

b)

$\theta=\frac{3\pi}{4},\frac{7\pi}{4}$

c)

$\theta=\frac{\pi}{3},\frac{4\pi}{3}$

d)

$\theta=\frac{3\pi}{4},\frac{4\pi}{3}$

14.

Solve equation for $0\le\theta<2\pi$ .
$1=5-8\cos\theta$

a)

$\theta=\frac{\pi}{6},\frac{\pi}{3},\frac{11\pi}{6}$

b)

$\theta=\frac{\pi}{6},\frac{11\pi}{6}$

c)

$\theta=\frac{\pi}{6}$

d)

$\theta=\frac{\pi}{3},\frac{5\pi}{3}$

15.

Solve equation for $0\le\theta<2\pi$ .
$-2=-5+3\sec\theta$

a)

$\theta=0,\frac{\pi}{3}$

b)

$\theta=0$

c)

$\theta=\frac{\pi}{3},\frac{5\pi}{3}$

d)

$No\ Solution$

16.

Solve equation for $0\le\theta<2\pi$ .
$-\sin^2\theta=\sin\theta+1-3\sin^2\theta$

a)

$\theta=\frac{\pi}{2},\frac{11\pi}{6}$

b)

$\theta=\frac{\pi}{2},\frac{7\pi}{6},\frac{11\pi}{6}$

c)

$\theta=\frac{2\pi}{3},\frac{7\pi}{6}$

d)

$\theta=0,\frac{2\pi}{3},\frac{4\pi}{3}$

Sum and Difference, Double Angle, Inverse Trig Quiz

Total questions: 16

Worksheet time: 2hrs 39mins

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