Trigonometry - Trigonometric Graphs and Parameters

The Singapore Flyer is the world’s largest Ferris Wheel as in year 2008. Its wheel has a radius of 75 m and makes a complete revolution in 30 minutes. The bottom of the wheel is 15m above ground. Let \(h\) m be the height of a passenger above ground \(t\) minutes after boarding a compartment at the bottom of the wheel.

1. Express \(h\) as a sine or cosine function of \(t\).
2. Find the height of the passenger above ground after
   1. 7.5 minutes,
   2. 15 minutes,
   3. 20 minutes.
3. Sketch the graph of the function in (a) for \( 0 \leq t \leq 30\).
4. Find the interval of time that the passenger is above 100 m from the ground.