Question 4 - A-Level Maths

Express \(9 \sin \theta - 12 \cos \theta\) in the form \(R \sin ( \theta - \alpha )\), where \(R > 0\) and \(0 ^ { \circ } < \alpha < 90 ^ { \circ }\). Give the value of \(\alpha\) correct to 2 decimal places. Hence
solve the equation \(9 \sin \theta - 12 \cos \theta = 4\) for \(0 ^ { \circ } \leqslant \theta \leqslant 360 ^ { \circ }\),
state the largest value of \(k\) for which the equation \(9 \sin \theta - 12 \cos \theta = k\) has any solutions.