Free Printable Inverse Trig Functions

1.

Since $f\left(x\right)=\tan\left(x\right)$ is one to one, its inverse exists.

a)

True

b)

False

2.

Check all that apply to $F\left(x\right)=Tan\left(x\right)$

a)

$Tan\left(x\right)$ has a restricted domain: $-\frac{\pi}{2}<x<\frac{\pi}{2}$

b)

$Tan^{-1}\left(x\right)$ exists

c)

its range is $\left[-1,1\right]$

d)

$Tan\left(-\frac{\pi}{4}\right)=-1$

e)

The domain is restricted to QI and QIV on the unit circle.

3.

$F^{-1}\left(x\right)=Tan^{-1}\left(x\right)$

a)

The domain is $\left(-\infty,\propto\right)$

b)

The range is $-\frac{\pi}{2}<x<\frac{\pi}{2}$

c)

$Tan^{-1}\left(1\right)=\frac{\pi}{4}$

d)

$Tan^{-1}\left(\sqrt{3}\right)=\frac{\pi}{3}$

e)

$Tan^{-1}\left(-\frac{\sqrt{3}}{3}\right)=-\frac{\pi}{6}$

4.

Since $g\left(x\right)=\sin\left(x\right)$ is not one to one, it does not have an inverse.

a)

True

b)

False

5.

Check all that apply to $G\left(x\right)=Sin\left(x\right)$

a)

$Sin\left(x\right)$ has a restricted domain: $-\frac{\pi}{2}\le x\le\frac{\pi}{2}$

b)

$Sin^{-1}\left(x\right)$ exists

c)

its range is $\left[-1,1\right]$

d)

$Sin\left(\frac{\pi}{4}\right)=1$

e)

The domain is restricted to QI and QII on the unit circle.

6.

$G^{-1}\left(x\right)=Sin^{-1}\left(x\right)$

a)

The domain is $\left(-\infty,\propto\right)$

b)

The range is $-\frac{\pi}{2}<x<\frac{\pi}{2}$

c)

$Sin^{-1}\left(\frac{\sqrt{2}}{2}\right)=\frac{\pi}{4}$

d)

$Sin^{-1}\left(-\frac{\sqrt{3}}{2}\right)=-\frac{\pi}{3}$

e)

$Sin^{-1}\left(0\right)=0$

7.

Since $h\left(x\right)=\cos\left(x\right)$ is one to one, its inverse exists.

a)

True

b)

False

8.

Check all that apply to $H\left(x\right)=Cos\left(x\right)$

a)

$Cos\left(x\right)$ has a restricted domain: $-\frac{\pi}{2}\le x\le\frac{\pi}{2}$

b)

$Cos^{-1}\left(x\right)$ exists

c)

its range is $\left[-1,1\right]$

d)

$Cos\left(\frac{3\pi}{4}\right)=-\frac{\sqrt{2}}{2}$

e)

The domain is restricted to QI and QII on the unit circle.

9.

$H^{-1}\left(x\right)=Cos^{-1}\left(x\right)$

a)

The domain is $\left[-1,1\right]$

b)

The range is $0\le x\le\pi$

c)

$Cos^{-1}\left(0\right)=\pi$

d)

$Cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)=\frac{5\pi}{6}$

e)

$Cos^{-1}\left(\frac{\sqrt{3}}{2}\right)=\frac{\pi}{6}$

10.

Evaluate $\tan\left(Cos^{-1}\left(-\frac{3}{5}\right)\right)=$

a)

$-\frac{3}{5}$

b)

$\frac{3}{5}$

c)

$-\frac{4}{3}$

d)

$\frac{4}{3}$

e)

UNDEFINED

11.

Evaluate $Tan^{-1}\left(\sin\left(\frac{\pi}{2}\right)\right)=$

a)

$\frac{\pi}{6}$

b)

$\frac{\pi}{4}$

c)

$\frac{\pi}{3}$

d)

$\frac{\pi}{2}$

e)

$\pi$

12.

Evaluate $Cos^{-1}\left(-\frac{1}{2}\right)=$

a)

$\frac{\pi}{4}$

b)

$\frac{\pi}{3}$

c)

$\frac{\pi}{2}$

d)

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

e)

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

13.

Evaluate $Sin^{-1}\left(-\frac{\sqrt{3}}{2}\right)=$

a)

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

b)

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

c)

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

d)

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

e)

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

14.

Evaluate $\cos\left(Sin^{-1}\left(-\frac{1}{2}\right)\right)=$

a)

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

b)

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

c)

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

d)

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

e)

$1$

15.

Evaluate $Tan^{-1}\left(\sin\left(\frac{3\pi}{2}\right)\right)=$

a)

$\frac{\pi}{2}$

b)

$-\frac{\pi}{2}$

c)

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

d)

$\frac{\pi}{4}$

e)

UNDEFINED

16.

Evaluate $\sin\left(Tan^{-1}\left(-\frac{4}{3}\right)\right)=$

a)

$-\frac{4}{5}$

b)

$\frac{4}{5}$

c)

$-\frac{3}{4}$

d)

$\frac{3}{4}$

e)

UNDEFINED

17.

Evaluate $Cos^{-1}\left(\sin\left(\frac{4\pi}{3}\right)\right)=$

a)

$\frac{\pi}{6}$

b)

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

c)

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

d)

$\frac{11\pi}{6}$

e)

1

18.

Evaluate $\csc\left[Sin^{-1}\left(1\right)+2Tan^{-1}\left(-1\right)\right]=$

a)

$1$

b)

$-1$

c)

$0$

d)

UNDEFINED

19.

Use a calculator to find to the degrees to the nearest hundredth of the expression $Sin^{-1}\left(0.87\right)=$ (a) . (Do not enter any words in your answer.)

20.

Use a calculator to find the degrees to the nearest hundredth of the expression $Cos^{-1}\left(-\frac{3}{5}\right)=$ (a) . (Do not enter any words in your answer.)

Inverse Trig Functions

Total questions: 20

Worksheet time: 19mins

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