Exercises: Restrict Domain for Inverse Trig Functions

A function has an inverse only if it is one-to-one. Which test
determines whether a function is one-to-one from its graph?

The sine function $y = \sin(x)$ is periodic with period $2\pi$.
Draw a horizontal line at $y = 0.5$ across the sine graph.
How many times does this line intersect $y = \sin(x)$ on the
interval $[0, 4\pi]$?

For a function $f$, the notation $f^{-1}(x)$ means the inverse
function of $f$. Which expression is NOT the same as $\sin^{-1}(x)$?

Evaluate $\arcsin\!\left(\dfrac{1}{2}\right)$. Give your answer
in radians.

Evaluate $\arccos\!\left(\dfrac{1}{2}\right)$. Give your answer
in radians.

Use the summary table to answer: what is the range of $\arctan(x)$?

Evaluate $\arctan(1)$. Give your answer in radians.

Evaluate $\arcsin\!\left(-\dfrac{\sqrt{2}}{2}\right)$.
Give your answer in radians.