Problem

The diagram shows part of the curve with equation $y = k\sin\frac{1}{2}x$, where $k$ is a positive constant and $x$ is measured in radians. The curve has a minimum point $A$.

(a) State the coordinates of $A$.

(b) A sequence of transformations is applied to the curve in the following order.

Translation of 2 units in the negative $y$-direction

Reflection in the $x$-axis

Find the equation of the new curve and determine the coordinates of the point on the new curve corresponding to $A$.