New Zealand
Level 8 - NCEA Level 3

# Domain and Range of Inverse Trigonometric Functions

## Interactive practice questions

In order to find an inverse function for $f\left(x\right)=\sin x$f(x)=sinx we must first restrict its domain.

a

Restricting the domain of $f\left(x\right)$f(x) to which of the following intervals will allow us to find an inverse function?

$\left[-\pi,0\right]$[π,0]

A

$\left[0,\pi\right]$[0,π]

B

$\left[0,2\pi\right]$[0,2π]

C

$\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$[π2,π2]

D

$\left[-\pi,0\right]$[π,0]

A

$\left[0,\pi\right]$[0,π]

B

$\left[0,2\pi\right]$[0,2π]

C

$\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$[π2,π2]

D
b

State the domain of the inverse function $f^{-1}(x)=$f1(x)=$\sin^{-1}x$sin1x.

Domain: $\left[\editable{},\editable{}\right]$[,]

Range: $\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$[π2,π2]

Easy
Approx 2 minutes

In order to find an inverse function for $f\left(x\right)=\cos x$f(x)=cosx we must first restrict its domain.

Select the true statement.

In order to find an inverse function for $f\left(x\right)=\tan x$f(x)=tanx we must first restrict its domain.

### Outcomes

#### M8-2

Display and interpret the graphs of functions with the graphs of their inverse and/or reciprocal functions