# When sinx=0, what does x equal?

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24
May 24, 2016

$\sin x$ is known as a periodic function that oscillates at regular intervals.

It crosses the x-axis (i.e. it is $0$) at $x = 0 , \pi ,$ and $2 \pi$ in the domain $\left[0 , 2 \pi\right]$, and continues to cross the x-axis at every integer multiple of $\pi$.

graph{sinx [-10, 10, -5, 5]}

And if you click on the graph, you get:

So, whenever $\sin x = 0$, we have that:

$\textcolor{b l u e}{x = \pi \pm k \pi}$ for all $k$ in the set of integers.

That is, if $k = 0 , 1 , 2 , . . . , N$, where $N$ is some arbitrarily large integer, then $\sin x = 0$ for $x = 0 , \pm \pi , \pm 2 \pi , . . . , \pm 2 N \pi$.

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5
May 19, 2017

#### Answer:

0° or any multiple of 180°

If $\sin x = 0$, then x = 0°

#### Explanation:

If you know that $\sin x = 0$, t
Then you need to use a process called 'arcsin'.
It might be shown as "arcs" or "asin" or similar.

This is shown as ${\sin}^{-} 1$ on many calculators and is not to be confused with $\frac{1}{\sin}$ which is the same as $\text{cosec}$

To find which angle(s) will have a sine value of $0$.

Depending on what type of calculator you have you key in one of the following:

• $\text{shift} \sin 0 =$ and you get the answer 0°

• $0 \text{ shift} \sin$ the display will read $0$

Any angle which is a multiple of 180° will also have a sin value of $0$

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