Question

How does $$\sin x=0$$ equals $$\pi$$?

Answer 1

Hint: In this problem, we have to find how $$\sin x=0$$ equals $$\pi$$. We should always know that the sine value is always equal to zero for every multiple of $$\pi$$, where $$\pi$$ radians is equal to $${180}^{\circ }$$. We can now draw a graph with a sine curve to see the value of sine for $$\pi$$.

Complete step by step answer:
We know that the given trigonometric function given is sine.
We should always remember that the sine value is always equal to zero for every multiple of $$\pi$$, where $$\pi$$ radians is equal to $${180}^{\circ }$$.
We can now draw a graph with a sine curve to see the value of sine for $$\pi$$.

We can now see that the sine curve touches the line at 0 in every multiple of $$\pi$$.
We can now write it as,
$$\Rightarrow \sin x=0\to x=k\times \pi$$
Where k is any whole number.
Therefore, we can summarize that every multiple of $$\pi$$ for the sine function is always equal to zero.

Note: Students should also remember that $$\pi$$ radians is equal to $${180}^{\circ }$$. We should also know that the sine function goes from 0 to $${90}^{\circ }={\displaystyle \frac{\pi }{2}}$$and then back to 0 to $${180}^{\circ }=\pi$$, and when we come down to -1 to $${270}^{\circ }={\displaystyle \frac{3\pi }{2}}$$ and when we go up to 0 again at $${360}^{\circ }=2\pi$$, therefore, it will be 0 at every multiple of $$\pi$$. We should also concentrate in the graph part while drawing the sine curve.