Trigonometry - Trigonometric Graphs and Parameters

The following diagram represent a large Ferris wheel, with a diameter of 100 metres.

Let \(P\) be a point on the wheel. The wheel starts with \(P\) at the lowest point, at ground level. The wheel rotates at a constant rate, in an anticlockwise (counterclockwise) direction. One revolution takes \(20\) minutes.

1. Write down the height of \(P\) above ground level after
   1. \(10\) minutes;
   2. \(15\) minutes.[2]

Let \(h(t)\) metres be the height of \(P\) above ground level after \(t\) minutes. Some values of \(h(t)\) are given in the table below.

2. 1. Show that \(h(8)=90.5\).
   2. Find \(h(21)\).[4]
3. Sketch the graph of \(h\), for \(0\leq t \leq 40\).[3]
4. Given that \(h\) can be expressed in the form \(h(t)=a\cos{bt}+c\), find \(a\), \(b\) and \(c\).[5]