- (a) Express \(6 \cos \theta + 8 \sin \theta\) in the form \(R \cos ( \theta - \alpha )\), where \(R > 0\) and \(0 < \alpha < \frac { \pi } { 2 }\).
Give the value of \(\alpha\) to 3 decimal places.
(b)
$$\mathrm { p } ( \theta ) = \frac { 4 } { 12 + 6 \cos \theta + 8 \sin \theta } , \quad 0 \leqslant \theta \leqslant 2 \pi$$
Calculate
- the maximum value of \(\mathrm { p } ( \theta )\),
- the value of \(\theta\) at which the maximum occurs.