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

Geometry Level 4

$$(\text{i})$$ 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.

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

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