Solve, for 0⩽x<360∘0 \leqslant x < 360^\circ0⩽x<360∘, the equation 5sinxtanx=2cosx+25\sin x \tan x = 2\cos x + 25sinxtanx=2cosx+2, giving your answers to one decimal place where appropriate.
The vertical displacement, hhh metres, of a sensor-buoy in a wave tank is modelled by the equation
h=4+Acos(12t−π5) h = 4 + A \cos\left(\frac{1}{2}t - \frac{\pi}{5}\right) h=4+Acos(21t−5π)where ttt is the time in seconds after the wave generator is activated, and AAA is a constant. The points PPP, QQQ, and RRR represent the first maximum, the subsequent minimum, and the next point where the buoy is at sea level (h=0h=0h=0) respectively.
Given that the maximum height reached by the buoy is 11 m: state the value of AAA,
find the exact coordinates of the minimum point QQQ,
find the value of ttt at RRR, giving your answer to 3 significant figures.
Practise AQA A Level Maths 1.8 E: Trigonometry with exam-style questions for A Level Maths. 239 questions covering 1.8.1 Trigonometric definitions, rules and radians, 1.8.2 Small angle approximations (A-level only), 1.8.3 Trigonometric functions and exact values, 1.8.4 Reciprocal and inverse trigonometric functions (A-level only), 1.8.5 Trigonometric identities, 1.8.6 Compound and double angle formulae (A-level only), 1.8.7 Solving trigonometric equations, 1.8.8 Proofs with trigonometric identities, and 1.8.9 Trigonometry in context, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
