IB AA HL May 2026 P2 TZA 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. \(P\) is a point on the wheel. The wheel starts moving with \(P\) at the lowest point and completes one revolution in \(4\) minutes.

The height, \(h\) metres, of \(P\) 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 \(c\).[4]
2. The height can also be given as \(h(t)=a-b\sin(c(t+d))^\circ\), where \(d\in\mathbb{Z}^+\).
   Find the smallest positive value of \(d\).[2]