# Exam-Style Question on Trig Graphs

## A mathematics exam-style question with a worked solution that can be revealed gradually

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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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