Review question

How many solutions does $\cos (\sin x)=\frac{1}{2}$ have? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R8386

Suggestion

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 $x$?