Target Mathematics

1.13: Quadratic in sin and tan double-angle equation

0606/12/M/J/18 — Question 8 · 8 marks

(a)
Solve 3cos⁡2θ+4sin⁡θ=43\cos^{2}\theta + 4\sin\theta = 4 for 0°≤θ≤180°0^{\degree} \le \theta \le 180^{\degree}.
[4]
(b)
Solve sin⁡2ϕ=3cos⁡2ϕ\sin 2\phi = \sqrt{3}\cos 2\phi for −π2≤ϕ≤π2-\tfrac{\pi}{2} \le \phi \le \tfrac{\pi}{2} radians.
[4]