Free Printable Inverse Trig Functions

Free Printable Worksheets

Worksheets

Inverse Trig Functions

Total questions: 29

Worksheet time: 32mins

Name

Class

Date

1.

sin[arcsin( $\frac{1}{2}$ )]

a)

$\frac{\pi}{6}$

b)

$\frac{1}{2}$

c)

$60\degree$

d)

no solution

2.

arccos[cos( $\frac{7\pi}{4}$ )]

a)

$\frac{\pi}{4}$

b)

$-\frac{\pi}{4}$

c)

$\frac{7\pi}{4}$

d)

$\frac{3\pi}{4}$

3.

tan[arctan(10)]

a)

no solution

b)

-10

c)

$\frac{1}{10}$

d)

10

4.

arcsin[sin( $\frac{4\pi}{3}$ )]

a)

$\frac{\pi}{3}$

b)

$-\frac{\pi}{3}$

c)

$\frac{4\pi}{3}$

d)

$\frac{5\pi}{3}$

5.

cos[arccos(-2)]

a)

-2

b)

no solution

c)

2

d)

$\frac{1}{2}$

6.

arcsin[sin( $\frac{\pi}{6}$ )]

a)

$\frac{1}{2}$

b)

$\frac{\pi}{6}$

c)

$-\frac{\pi}{6}$

d)

no solution

7.

arccos[cos( $\frac{2\pi}{3}$ )]

a)

$\frac{2\pi}{3}$

b)

$\frac{\pi}{3}$

c)

$\frac{1}{2}$

d)

no solution

8.

arctan[tan( $\frac{5\pi}{4}$ )]

a)

$-\frac{\pi}{4}$

b)

$\frac{\pi}{4}$

c)

$\frac{5\pi}{4}$

d)

$\frac{3\pi}{4}$

9.

cos[arccos( $\frac{1}{3}$ )]

a)

3

b)

$\frac{1}{3}$

c)

-3

d)

no solution

10.

sin[arcsin(0.11)]

a)

no solution

b)

11

c)

0.11

d)

-0.11

11.

arcsin[sin( $\frac{\pi}{3}$ )]

a)

$\frac{2\pi}{3}$

b)

$-\frac{\pi}{3}$

c)

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

d)

$\frac{\pi}{3}$

12.

arccos[cos( $\frac{11\pi}{6}$ )]

a)

$\frac{5\pi}{6}$

b)

$\frac{\pi}{6}$

c)

$-\frac{\pi}{6}$

d)

$\frac{7\pi}{6}$

13.

arctan[tan( $\frac{2\pi}{3}$ )]

a)

$-\frac{\pi}{3}$

b)

$\frac{\pi}{3}$

c)

$\frac{5\pi}{3}$

d)

$\frac{2\pi}{3}$

14.

What are the domain and range of y = arccos(x)

a)

domain [-1, 1] range [-2π, 2π]

b)

domain [-1, 1] range [0, π]

c)

domain [-1, 1] range [-π/2, π/2]

d)

domain [0, 2π] range [-1, 1]

15.

What are the domain and range of y = arctan(x)

a)

domain [-1, 1] range [-2π, 2π]

b)

domain (-∞, ∞) range [-π/2, π/2]

c)

domain [-1, 1] range (-π/2, π/2)

d)

domain (-∞, ∞) range (-π/2, π/2)

16.

$\tan^{-1}\left(\sec\pi\right)$

a)

135°, 315°

b)

90°, 270°

c)

45°, 135°

d)

45°, 315°

17.

$\tan^{-1\ }\left(\csc\ -\frac{\pi}{2}\right)$

a)

135°, 315°

b)

45°, 225°

c)

90°, 270°

d)

45°, 135°

18.

$\tan^{-1}\left(\cos\ 0\right)$

a)

45°, 225°

b)

0°, 270°

c)

45°, 315°

d)

0°, 180°, 360°

19.

$\sin^{-1}\ \left(\cos\ \frac{\pi}{6}\right)$

a)

60°, 120°

b)

30°, 150°

c)

45°, 135°

d)

120°, 150°

20.

csc(cos^-1(√(3)/2))

a)

2

b)

-2

c)

2√3/3

d)

-2√3/3

21.

tan(sin^-1(-1/2))

a)

√3

b)

√3/3

c)

-√3

d)

-√3/3

22.

tan(sin^-1(-1/2))

a)

√3

b)

√3/3

c)

-√3

d)

-√3/3

23.

Evaluate the function: arcsin(-1/2)

a)

π/3

b)

π/6

c)

5π/6

d)

-π/6

24.

a)

A

b)

B

c)

C

d)

D

25.

cos^-1[tan(-π/4)] =

a)

0

b)

π

c)

π/4

d)

3π/4

26.

arcsin[sin( $\frac{\pi}{6}$ )]

a)

$\frac{1}{2}$

b)

$\frac{\pi}{6}$

c)

$-\frac{\pi}{6}$

d)

no solution

27.

Find the exact value of the composite function.

\sin\left[\sin^{-1}\left(-2\right)\right]

a)

2

b)

$-\frac{1}{2}$

c)

-2

d)

Not defined

28.

Find the exact value of the composite function.

\sin\left(\cos^{-1}\ \frac{1}{2}\right)

a)

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

b)

$\frac{1}{2}$

c)

$\frac{\pi}{6}$

d)

$\frac{\pi}{3}$

29.

Find the exact value of the composite function.

\sec\left(\tan^{-1}\sqrt{3}\right)

a)

2

b)

$\frac{1}{2}$

c)

-2

d)

Not defined

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