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

which formula gives the zeros of y = sin(x)?\no (kpi) for any positive integer k\no (kpi) for any integer k\no (\frac{kpi}{2}) for any positive integer k\no (\frac{kpi}{2}) for any integer k

which formula gives the zeros of y = sin(x)?\no (kpi) for any positive integer k\no (kpi) for any integer k\no (\frac{kpi}{2}) for any positive integer k\no (\frac{kpi}{2}) for any integer k

Answer

Answer:

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

Explanation:

Step1: Recall sine - function property

The sine function $y = \sin(x)$ has a value of 0 when $x$ is an integer multiple of $\pi$. Mathematically, $\sin(k\pi)=0$, where $k\in\mathbb{Z}$ (the set of all integers). This is because the sine - function represents the $y$ - coordinate of a point on the unit circle. At angles $x = 0,\pm\pi,\pm2\pi,\cdots$, the $y$ - coordinate of the corresponding points on the unit circle is 0. When $k$ is a positive integer, we have $x=\pi,2\pi,3\pi,\cdots$; when $k$ is a negative integer, we have $x =-\pi,- 2\pi,\cdots$; and when $k = 0$, $x = 0$. So the zeros of $y=\sin(x)$ are given by $x = k\pi$ for any integer $k$.