## Exam-Style Question on Sinusoidal Modelling## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 350. This question is similar to one that appeared on an IB Standard paper in 2018. The use of a calculator is allowed.

A Big Wheel at an amusement park has a diameter of length 70 metres which rotates at a constant speed. The bottom of the wheel is h metres above the ground. A seat starts at the bottom of the wheel.The wheel completes one revolution in 4 minutes. [The diagram is not to scale]

(a) After 2 minutes, the seat is 76m above the ground. Find h.

(b) After t minutes, the height of the seat above ground is given by \(f(t) =41+ k \cos{ \frac{\pi t}{2}} \) for \(0 \le t \le 16 \).

Find the value of k.

(c) Find when the seat is 40 m above the ground for the third time.

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