The diagram shows a section of the curve with equation $y = k\sin\left(\frac{1}{2}x\right)$, where $k$ is a positive constant and $x$ is measured in radians. Point $A$ is a minimum point on the curve.
(a)[1]
State the coordinates of $A$.
(b)[3]
The curve is transformed in this order: first translated 2 units in the negative $y$-direction; then reflected in the $x$-axis. Determine the equation of the resulting curve and the coordinates of the point on it that corresponds to $A$.
Worked solution & mark scheme
This 4-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State the point as $(3\pi, -k)$.” …