# Exam-Style Question on Circular functions

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 37. This question is similar to one that appeared on an IB Standard paper in 2013. The use of a calculator is allowed.

The Big Wheel at Fantasy Fun Fayre rotates clockwise at a constant speed completing 15 rotations every hour. The wheel has a diameter of 90 metres and the bottom of the wheel is 6 metres above the ground.

A cabin starts at the bottom of the wheel with the top of the cabin 6m above the ground.

(a) Find the greatest height of the top of the cabin reaches as the wheel rotates.

After $$t$$ minutes, the height $$h(t)$$ metres above the ground of the top of a cabin is given by the function $$h(t)=51-a\cos bt$$.

(b) Find the period of $$h(t)$$

(c) Find the value of $$b$$.

(d) Find the value of $$a$$.

(e) Sketch the graph of $$h(t)$$ , for $$0\le t\le 5$$.

(f) In one rotation of the wheel, find the probability that a randomly selected seat is at least 70 metres above the ground. Give your answer to two decimal places.

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