9. Solutions based entirely on graphical or numerical methods are not acceptable in this question.
- Solve, for \(0 \leqslant \theta < 180 ^ { \circ }\), the equation
$$3 \sin \left( 2 \theta - 10 ^ { \circ } \right) = 1$$
giving your answers to one decimal place.
- The first three terms of an arithmetic sequence are
$$\sin \alpha , \frac { 1 } { \tan \alpha } \text { and } 2 \sin \alpha$$
where \(\alpha\) is a constant.
(a) Show that \(2 \cos \alpha = 3 \sin ^ { 2 } \alpha\)
Given that \(\pi < \alpha < 2 \pi\),
(b) find, showing all working, the value of \(\alpha\) to 3 decimal places.