6 A tourist attraction in a city centre is a big vertical wheel on which passengers can ride. The wheel turns in such a way that the height, \(h \mathrm {~m}\), of a passenger above the ground is given by the formula \(h = 60 ( 1 - \cos k t )\). In this formula, \(k\) is a constant, \(t\) is the time in minutes that has elapsed since the passenger started the ride at ground level and \(k t\) is measured in radians.

1. Find the greatest height of the passenger above the ground. One complete revolution of the wheel takes 30 minutes.
2. Show that \(k = \frac { 1 } { 15 } \pi\).
3. Find the time for which the passenger is above a height of 90 m .