Exam-Style Question on Circular functions
A mathematics exam-style question with a worked solution that can be revealed gradually
Question id: 461. This question is similar to one that appeared on an A-Level paper (specimen) for 2017. The use of a calculator is allowed.
The height above the ground, H metres, of a passenger on a Ferris wheel t minutes after the wheel starts turning, is modelled by the following equation:$$H = k – 8\cos (60t)° + 5\sin (60t)°$$
where k is a constant.
(a) Express \(H\) in the form \(H = k - R \cos(60t + a)° \) where \(R\) and \(a\) are constants to be found (\( 0° \lt a \lt 90° \)).
(b) Given that the initial height of the passenger above the ground is 2 metres, find a complete equation for the model.
(c) Hence find the maximum height of the passenger above the ground.
(d) Find the time taken for the passenger to reach the maximum height on the fifth cycle. (Solutions based entirely on graphical or numerical methods are not acceptable.)
(e) It is decided that, to increase profits, the speed of the wheel is to be increased. How would you adapt the equation of the model to reflect this increase in speed?
The worked solutions to these exam-style questions are only available to those who have a Transum Subscription.
Subscribers can drag down the panel to reveal the solution line by line. This is a very helpful strategy for the student who does not know how to do the question but given a clue, a peep at the beginnings of a method, they may be able to make progress themselves.
This could be a great resource for a teacher using a projector or for a parent helping their child work through the solution to this question. The worked solutions also contain screen shots (where needed) of the step by step calculator procedures.
A subscription also opens up the answers to all of the other online exercises, puzzles and lesson starters on Transum Mathematics and provides an ad-free browsing experience.
Drag this panel down to reveal the solution
©1997 - 2021 Transum Mathematics :: For more exam-style questions and worked solutions go to Transum.org/Maths/Exam/