on the interval 0 ≤ x ≤ 2π, what are the x - intercepts of y = sinx?\n0, $\frac{pi}{2}$, and…

on the interval 0 ≤ x ≤ 2π, what are the x - intercepts of y = sinx?\n0, $\frac{pi}{2}$, and $\frac{3pi}{2}$\n0, π, and 2π\n$\frac{pi}{2}$ and $\frac{3pi}{2}$ only\nπ and 2π only

on the interval 0 ≤ x ≤ 2π, what are the x - intercepts of y = sinx?\n0, $\frac{pi}{2}$, and $\frac{3pi}{2}$\n0, π, and 2π\n$\frac{pi}{2}$ and $\frac{3pi}{2}$ only\nπ and 2π only

Answer

Explanation:

Step1: Recall x - intercept definition

The x - intercepts of a function (y = f(x)) are found by setting (y = 0). So for (y=\sin x), we set (\sin x=0).

Step2: Use sine - function properties

We know that (\sin x = 0) when (x = k\pi), where (k\in\mathbb{Z}) (the set of integers).

Step3: Find values in given interval

For the interval (0\leq x\leq2\pi), when (k = 0), (x=0); when (k = 1), (x=\pi); when (k = 2), (x = 2\pi).

Answer:

B. (0,\pi, \text{ and }2\pi)