which formula gives the zeros of y = sin(x)?\no kπ for any positive integer k\no kπ for any integer k\no…

Answer:

B. $k\pi$ for any integer $k$

Explanation:

Step1: Recall sine - function property

The sine function $y = \sin(x)$ has zeros when $x$ is an integer multiple of $\pi$. We know that $\sin(0)=0$, $\sin(\pi)=0$, $\sin(-\pi)=0$, $\sin(2\pi)=0$, $\sin(- 2\pi)=0$ and in general, for $x = k\pi$, where $k\in\mathbb{Z}$ (the set of all integers), $\sin(k\pi)=0$. When $k = 0$, $\sin(0)=0$; when $k = 1$, $\sin(\pi)=0$; when $k=-1$, $\sin(-\pi)=0$ etc. If we consider $\frac{k\pi}{2}$, when $k = 1$, $\sin(\frac{\pi}{2}) = 1\neq0$, when $k = 3$, $\sin(\frac{3\pi}{2})=-1\neq0$. So the zeros of $y=\sin(x)$ are given by $x = k\pi$ for any integer $k$.