Which formula gives the zeros of \( y=\sin (x) \) ? \( k \pi \) for any positive integer \( k \) \( k \pi \) for any integer \( k \) \( \frac{k \pi}{2} \) for any positive integer \( k \) \( \frac{k \pi}{2} \) for any integer \( k \)

To find the zeros of \( y = \sin(x) \), we need the values of \( x \) for which \( \sin(x) = 0 \). The sine function is zero at every integer multiple of \( \pi \). So, the correct formula for the zeros of the equation is \( k \pi \) for any integer \( k \). This includes positive integers, negative integers, and zero itself! If you're looking to visualize this, think about a graph of the sine function. The waves cross the x-axis at \( 0, \pi, 2\pi, -\pi, -2\pi \) and so on, creating those infinite beautiful oscillations. Each zero represents a point of equilibrium in the wave!