How many solutions does $\cos (\sin x)=\frac{1}{2}$ have?

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In the range \(0 \le x < 2\pi\) the equation \[\cos(\sin x) = \frac{1}{2}\] has

1. no solutions;

2. one solution;

3. two solutions;

4. three solutions.

First consider \[\cos y = \frac{1}{2};\] what are the solutions of this equation?

From this, can you find the values of \(\sin x\) that satisfy \[\cos(\sin x) = \frac{1}{2}?\]

Do all or any of these values of \(\sin x\) give a solution for \(x\)?