What is the number of possible $ x$ values in $\frac{x}{100}= \sin(x)$ Problem
 $\frac{x}{100}= \sin(x)$ We are asked to find the number of possible values of $x$ in this scenario and I had tried to figure it out by the use of trigonometric identities but then i had realized that there are no trig identities that can help me... or is there?

steps that i had tried:
I first multiplied 100 on both sides to get $x$ by itself to get:
$100(\sin x)=x$

Then i determined that $\sin x \le 1$ therefore I had determined that $\frac{x}{100}$ is $\le 1$

But when i look at the answer choices all of them are less than $100$ meaning that all of them are going to make $\frac{x}{100}$ less than 100 when $x$ is substituted.
Since $|\sin x|\le 1$, one needs only to consider $\frac{|x|}{100} \le 1$, or $|x|\le 100$. Since both functions are odd, we restrict ourselves to the interval $[0,100]$. The curve 

$$\tag{1} y = \frac{ x}{100}$$

is positive on $(0,100]$. $\sin x$ is periodic with period $2\pi$. On each (half) period

$$[0,\pi], [2\pi, 3\pi], \cdots [2n\pi, (2n+1)\pi]$$

as long as $(2n+1) \pi &lt;100$, the curve $(1)$ intersects $\sin x$ at $2$ points. Since $15.5&lt; 100/2\pi &lt;16$, this means that there are $32$ nonnegative solution and thus $63$ solution in the real line.
look at this site body must be [1]: https://www.wolframalpha.com/input/?i=x%2F100%20%3D%20sin(x)