Double angle equations

1 Solve the equation \(\sin 2 x = 2 \cos 2 x\), for \(0 ^ { \circ } \leqslant x \leqslant 180 ^ { \circ }\).

2 Solve the equation \(5 \tan 2 \theta = 4 \cot \theta\) for \(0 ^ { \circ } < \theta < 180 ^ { \circ }\).

2 Solve the equation $$\sin \theta = 2 \cos 2 \theta + 1$$ giving all solutions in the interval \(0 ^ { \circ } \leqslant \theta \leqslant 360 ^ { \circ }\).

3 Solve the equation $$\cos \theta + 4 \cos 2 \theta = 3$$ giving all solutions in the interval \(0 ^ { \circ } \leqslant \theta \leqslant 180 ^ { \circ }\).

3 Solve the equation $$\cos \theta + 3 \cos 2 \theta = 2$$ giving all solutions in the interval \(0 ^ { \circ } \leqslant \theta \leqslant 180 ^ { \circ }\).

3 Find the values of \(x\) satisfying the equation $$3 \sin 2 x = \cos x$$ for \(0 ^ { \circ } \leqslant x \leqslant 90 ^ { \circ }\).

3 Solve the equation $$2 \cos 2 \theta = 4 \cos \theta - 3$$ for \(0 ^ { \circ } \leqslant \theta \leqslant 180 ^ { \circ }\).

1. (a) Show that the equation

$$\tan 2 x = 5 \sin 2 x$$ can be written in the form $$( 1 - 5 \cos 2 x ) \sin 2 x = 0$$ (b) Hence solve, for \(0 \leqslant x \leqslant 180 ^ { \circ }\), $$\tan 2 x = 5 \sin 2 x$$ giving your answers to 1 decimal place where appropriate.
You must show clearly how you obtained your answers.

2. Solve, for \(0 \leqslant \theta < 2 \pi\), $$2 \cos 2 \theta = 5 - 13 \sin \theta$$ Give your answers in radians to 3 decimal places.
(Solutions based entirely on graphical or numerical methods are not acceptable.)

1. Find all the solutions of

$$2 \cos 2 \theta = 1 - 2 \sin \theta$$ in the interval \(0 \leqslant \theta < 360 ^ { \circ }\).

4 Solve the equation \(2 \sin 2 \theta + \cos 2 \theta = 1\), for \(0 ^ { \circ } \leqslant \theta < 360 ^ { \circ }\).

3 Solve the equation \(\cos 2 \theta = \sin \theta\) for \(0 \leqslant \theta \leqslant 2 \pi\), giving your answers in terms of \(\pi\).