ANSWER
Yes, it does
EXPLANATION
We want to know if the given function has infinite solutions:
[tex]\sin x=\frac{1}{2}[/tex]The given function is a periodic function. It has a period of 2π radians (360 degrees).
This implies that for every revolution from a solution of the given function, there is another value of x which has the exact same function.
In other words, there are infinite values of x for which its sine is 1/2.
Therefore, it has infinite solutions.