Trigonometry in contextEdexcel A-Level Maths: Flashcards

What these 13 flashcards ask

Period of y=\sin(ct) in degrees and radians?
Greatest and least values of a+b\sin(ct+d) with b0?
Amplitude of 6-5\cos(30t)^\circ?
Period of 6-5\cos(30t)^\circ?
Why is h=6-5\cos(30t)^\circ lowest at t=0?
What should you check before using trig on a calculator?
If the angle is ct+d, how do you find the range to use?
A force F at \theta above horizontal: components?
Projectile range on level ground?
Two angles that give the same range?
For 12+4\sin x14, what must \sin x be?
Why can a trig model fail in reality?
How to find the greatest value of 3\sin x+4\cos x?

Exam questions on Trigonometry in context

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
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
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

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).