14. In this question solutions based entirely on graphical or numerical methods are not acceptable.
- Solve, for \(- 180 ^ { \circ } \leqslant x < 180 ^ { \circ }\), the equation
$$\sin \left( x + 60 ^ { \circ } \right) = - 0.4$$
giving your answers, in degrees, to one decimal place.
- (a) Show that the equation
$$2 \sin \theta \tan \theta - 3 = \cos \theta$$
can be written in the form
$$3 \cos ^ { 2 } \theta + 3 \cos \theta - 2 = 0$$
(b) Hence solve, for \(0 \leqslant \theta < 360 ^ { \circ }\), the equation
$$2 \sin \theta \tan \theta - 3 = \cos \theta$$
showing each stage of your working and giving your answers, in degrees, to one decimal place.