OCR A Level: Core 3 - Trigonometry [June 2009 Q7]

$(\text{i})$ Express $8 \sin \theta - 6 \cos \theta$ in the form $R \sin (\theta - \alpha)$ , where $R>0$ and $0°< \alpha < 90°$ .

$(\text{ii})$ Hence

$(\textbf{a})$ solve, for $0°<\theta<360°$ , the equation $8 \sin \theta - 6 \cos \theta = 9$

$(\textbf{b})$ find the greatest possible value of $32 \sin x - 24 \cos x - (16 \sin y - 12 \cos y)$ as the angles $x$ and $y$ vary.

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Input your answer to part $(\text{ii}) (\textbf{b})$ .

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There are 3 marks available for part (i), 4 marks for part (ii) (a) and 3 marks for part (ii) (b).

In total, this question is worth 13.9% of all available marks in the paper.

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This is part of the set OCR A Level Problems .