Additional Mathematics 4037: Trigonometry Topical Past Paper Questions

Solve the equation $ \sec^{2}3x + \tan 3x - 3 = 0 $ for $ 0^{\circ} \leq x \leq 120^{\circ} $.

(a) Solve the equation $ \sin 4x = \frac{1}{2} $ for $ 0 \leq x \leq \frac{\pi}{4} $, giving your answers in terms of $ \pi $. [2] (b) The diagram shows parts of the graphs of $y=\sin4x$ and $y=\frac{1}{2}$. Find the exact area of the shaded region enclosed by the curve and the l…

(a) Show that $ \frac{\sin x}{\tan x-1}-\frac{\cos x}{\tan x+1}=\frac{\cos x}{\sin^{2}x-\cos^{2}x} $. [5] (b) Hence solve the equation $ \frac{\sin x}{\tan x-1}-\frac{\cos x}{\tan x+1}=1 $ for $ 0^{\circ}<x<360^{\circ} $. [5]