# Exam-Style Questions on Trig Graphs

## Problems on Trig Graphs adapted from questions set in previous Mathematics exams.

### 1.

IB Standard

(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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The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

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