Express \(\sin 2 x\) in terms of \(\sin x\) and \(\cos x\).
Solve the equation
$$5 \sin 2 x + 3 \cos x = 0$$
giving all solutions in the interval \(0 ^ { \circ } \leqslant x \leqslant 360 ^ { \circ }\) to the nearest \(0.1 ^ { \circ }\), where appropriate.
Given that \(\sin 2 x + \cos 2 x = 1 + \sin x\) and \(\sin x \neq 0\), show that \(2 ( \cos x - \sin x ) = 1\).