Mathematics 9709 · AS & A Level · Trigonometry

Trigonometry — practice question

(i)[3]

Write $2\sin\theta - \cos\theta$ in the form $R\sin(\theta - \alpha)$, where $R > 0$ and $0^\circ < \alpha < 90^\circ$, and give the exact value of $R$ together with $\alpha$ correct to $2$ decimal places.

(ii)[4]

Hence solve the equation $2\sin\theta - \cos\theta = -0.4$, and give every solution in the interval $0^\circ \leq \theta \leq 360^\circ$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Give $R=\sqrt5$

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