Question

on the interval $0 \leq x \leq 2\pi$, what are the $x$-intercepts of $y = \sin x$?
$\pi$ and $2\pi$ only
$\frac{\pi}{2}$ and $\frac{3\pi}{2}$ only
$0$, $\pi$, and $2\pi$
$0$, $\frac{\pi}{2}$, and $\frac{3\pi}{2}$

Explanation:

Step1: Define x-intercept condition

x-intercepts occur where $y=0$, so set $\sin x = 0$.

Step2: Solve for x in given interval

Find $x$ such that $0 \leq x \leq 2\pi$ and $\sin x = 0$. The solutions are $x=0$, $x=\pi$, $x=2\pi$.

Answer:

0, $\pi$, and $2\pi$