Mathematics 9709 · AS & A Level · Trigonometry

Trigonometry — practice question

The function $f(\theta)$ is given by $f(\theta) = 12 \sin \theta \cos \theta + 16 \cos^2 \theta$.
(a)[5]

Write $f(\theta)$ in the form $R \cos(2\theta - \alpha) + k$, where $R > 0$, $0 < \alpha < \frac{1}{2}\pi$ and $k$ is a constant. Give the values of $R$ and $k$, and state $\alpha$ correct to 4 significant figures.

(b)[3]

Find the least positive value of $\theta$ for which the equation $f(\theta) = 17$ is satisfied.

(c)[2]

Determine $\int f(\theta) \, d\theta$.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Use the correct identity for either $\sin 2\theta$ or $\cos 2\theta$

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