Observation wheel capsule height modelled by a cosine function and an equivalent sine phase shift

An observation wheel of radius \(35\) metres turns at a constant rate about its centre, which is \(37\) metres above the ground. A capsule \(Q\) on the rim is at the bottom of the wheel when the wheel starts to turn, and the wheel takes \(20\) minutes to make one complete turn.

After \(t\) minutes, \(Q\) is \(h\) metres above the ground, where \(h=a-b\cos(ct)^\circ\) and \(a,b,c\in\mathbb{Z}^+\).

1. Find \(a\), \(b\) and \(c\).[4]

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

2. Find the least possible value of \(d\).[2]