3.
$$f ( x ) = 7 \cos x + \sin x$$
Given that \(\mathrm { f } ( x ) = R \cos ( x - \alpha )\), where \(R > 0\) and \(0 < \alpha < 90 ^ { \circ }\),
- find the exact value of \(R\) and the value of \(\alpha\) to one decimal place.
- Hence solve the equation
$$7 \cos x + \sin x = 5$$
for \(0 \leqslant x < 360 ^ { \circ }\), giving your answers to one decimal place.
- State the values of \(k\) for which the equation
$$7 \cos x + \sin x = k$$
has only one solution in the interval \(0 \leqslant x < 360 ^ { \circ }\)