2026 MAY TZA P2 Q3

A Ferris wheel with radius \(20\) metres rotates at a constant speed. The centre of the wheel is \(23\) metres above the ground, as shown in the following diagram. \(\mathrm{P}\) is a point on the wheel. The wheel starts moving with \(\mathrm{P}\) at the lowest point and completes on revolution in \(4\) minutes.

The height, \(h\) metres, of \(\mathrm{P}\) above the ground after \(t\) minutes is given by

\(h = a - b\cos({ct})^{\circ}\), where \(a, b, c \in \mathbb{Z}^+\).

1. Find the value of \(a\), the value of \(b\) and the value of \(c\).

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The heightcan also be given as \(h(t) = a - b\sin{ \left( c (t + d) \right)^{\circ}}\), where \( d \in \mathbb{Z}^+\).

2. Find the smallest positive value of \(d\).

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