Trigonometry in contextEdexcel A-Level Maths: Mind map

Exam questions on Trigonometry in context

1. The height $h$ metres above the ground of a point $P$ on the rim of a vertical wheel, $t$ seconds after the wheel starts to turn, is modelled by $h=6-5\cos(30t)^\circ$.
   Find the first time, to 3 significant figures, at which $P$ is $9$ m above the ground.2 marks
2. The number of hours of daylight, $D$, in a town on day $n$ of the year ($n=1$ is 1 January) is modelled by $D=12+4\sin\left(\dfrac{2\pi(n-80)}{365}\right)$, where the angle is in radians.
   Use the model to find, to the nearest day, the number of days in the year on which there are more than $14$ hours of daylight.2 marks
3. A ball is kicked from level ground with speed $20\ \text{m s}^{-1}$ at an angle $\alpha$ above the horizontal. Modelling the ball as a particle moving freely under gravity ($g=9.8\ \text{m s}^{-2}$), the horizontal distance it travels before landing is $R=\dfrac{400\sin2\alpha}{g}$ metres.
   The ball lands $30$ m away. Find the two possible values of $\alpha$, to 1 decimal place, with $0<\alpha<90^\circ$.3 marks