Question

The graph of the inverse trigonometric function can be obtained from the graph of their corresponding trigonometric function by interchanging $x$ and $y$ axes. State True/False.

Answer 1

If $(x_1,y_1)$ lies on $y=f\left(x\right)$

$\Rightarrow (y_1,x_1)$ lies on $y=f^{-1}\left(x\right)$

$\Rightarrow$ If a point lies on $y=f\left(x\right)$ and we interchange axes, then the new point lies on $y=f^{-1}\left(x\right)$

$\because (x_1,y_1)$ and $(y_1,x_1)$ are symmetric about $y=x$

$\Rightarrow y=f\left(x\right)$ and $y=f^{-1}\left(x\right)$ are symmetric about $y=x$

$\Rightarrow$ If we interchange axes, we can obtain the graph of inverse trigonometric functions from the graph of their corresponding trigonometric function.

Hence, the statement is true.