## Exam-Style Question on Trig Graphs## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 453. This question is similar to one that appeared on an IB Standard paper in 2009. The use of a calculator is allowed.

(a) Sketch the graph of \(f(x) = 4\sin x - 5\cos x \), for \(–2\pi \le x \le 2\pi \).

(b) Find the amplitude of \(f\).

(c) Find the the period of \(f\).

(d) Find the \(x\)-intercept that lies between 0 and 3.

(e) Hence write \(f(x)\) in the form \(a \sin (bx + c) \).

(f) Write down one value of \(x\) such that \(f'(x) = 0 \).

(g) Write down the two values of \(p\) for which the equation \(f(x) = p\) has exactly two solutions.

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