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Problem 541
541
The function \(f : x \mapsto 4 - 3 \sin x\) is defined for the domain \(0 \leq x \leq 2\pi\).
(i) Solve the equation \(f(x) = 2\). [3]
(ii) Sketch the graph of \(y = f(x)\). [2]
(iii) Find the set of values of \(k\) for which the equation \(f(x) = k\) has no solution. [2]
The function \(g : x \mapsto 4 - 3 \sin x\) is defined for the domain \(\frac{1}{2}\pi \leq x \leq A\).
(iv) State the largest value of \(A\) for which \(g\) has an inverse. [1]
(v) For this value of \(A\), find the value of \(g^{-1}(3)\). [2]
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