Consider the function $f: x \mapsto 4 - 3\sin x$, defined over the domain $0 \leq x \leq 2\pi$.
(i)[3]
Solve $f(x) = 2$.
(ii)[2]
Sketch the graph for $y = f(x)$.
(iii)[2]
Find the values of $k$ for which there is no solution to the equation $f(x) = k$.
(iv)[1]
The function $g: x \mapsto 4 - 3\sin x$ is defined on the domain $\tfrac{1}{2}\pi \leq x \leq A$. State the greatest value of $A$ for which $g$ has an inverse.
(v)[2]
For this value of $A$, determine $g^{-1}(3)$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Solve $4-3\sin x=2$ and hence deduce $\sin x=\frac23$.” …