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.
