2.
$$f ( x ) = 5 \cos x + 12 \sin x$$
Given that \(\mathrm { f } ( x ) = R \cos ( x - \alpha )\), where \(R > 0\) and \(0 < \alpha < \frac { \pi } { 2 }\),
- find the value of \(R\) and the value of \(\alpha\) to 3 decimal places.
- Hence solve the equation
$$5 \cos x + 12 \sin x = 6$$
for \(0 \leqslant x < 2 \pi\).
- Write down the maximum value of \(5 \cos x + 12 \sin x\).
- Find the smallest positive value of \(x\) for which this maximum value occurs.