Wind turbine blade tip height as a cosine model and the equivalent sine phase shift

The tip \(P\) of one blade of a wind turbine moves in a vertical circle about the hub. Each blade is \(42\) metres long, and the hub is \(75\) metres above the ground. The blades turn at a constant rate, making one complete turn every \(8\) seconds, and \(P\) is at its lowest position when \(t=0\).

The height of \(P\) above the ground, \(h\) metres, \(t\) seconds later is modelled by \(h=a-b\cos(ct)^\circ\), where \(a\), \(b\) and \(c\) are positive integers.

1. Find \(a\), \(b\) and \(c\).[4]
2. The same model can be written as \(h=a-b\sin\left(c(t+d)\right)^\circ\), where \(d\) is a positive integer.
   Find the least possible value of \(d\).[2]