Problem

The diagram shows two curves. One curve has equation $y = \sin x$ and the other curve has equation $y = f(x)$.

(a) In order to transform the curve $y = \sin x$ to the curve $y = f(x)$, the curve $y = \sin x$ is first reflected in the $x$-axis.

Describe fully a sequence of two further transformations which are required.

(b) Find $f(x)$ in terms of $\sin x$.