Inverse Trig Functions Flashcards

Question 1

State the domain and range of $\arcsin(x)$.

Accepted Answer

Domain: $[-1,1]$. Range: $\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$.

Question 2

Evaluate $\arcsin\left(\frac{\sqrt{3}}{2}\right)$.

Accepted Answer

$\frac{\pi}{3}$, since $\sin\left(\frac{\pi}{3}\right)=\frac{\sqrt{3}}{2}$ and $\frac{\pi}{3}\in\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$.

Question 3

Simplify $\cos(\arcsin x)$ for $x\in[-1,1]$.

Accepted Answer

$$\cos(\arcsin x)=\sqrt{1-x^2}$$
Because if $	heta=\arcsin x$ then $\sin	heta=x$ with $	heta\in\left[-\frac{\pi}{2},\frac{\pi}{2}ight]$, so $\cos	heta\ge 0$.

Inverse Trig Functions Flashcards

Master Math with AI

Learning Resources

Trusted & Recognized