Question 9 - A-Level Maths

Express \(3 \cos 3 x + 7 \sin 3 x\) in the form \(R \cos ( 3 x - \alpha )\), where \(R > 0\) and \(0 < \alpha < \frac { 1 } { 2 } \pi\).
Give full details of a sequence of three transformations needed to transform the curve \(y = \cos x\) to the curve \(y = 3 \cos 3 x + 7 \sin 3 x\).
Determine the greatest value of \(3 \cos 3 x + 7 \sin 3 x\) as \(x\) varies and give the smallest positive value of \(x\) for which it occurs.
Determine the least value of \(3 \cos 3 x + 7 \sin 3 x\) as \(x\) varies and give the smallest positive value of \(x\) for which it occurs.