# 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 \((\text{ii}) (\textbf{b})\).**