Trigonometry - Trigonometric Graphs and Parameters
Trigonometry - Trigonometric Graphs and Parameters
TGM Original Questions
The Singapore Flyer is one of the world's most famous Ferris wheels, which has a radius of \(75\) m and its centre is \(90\) m above the ground. It makes a complete revolution in \(30\) minutes. Let \(h\) m be the height of a passenger above the ground \(t\) minutes after boarding at the bottom of the wheel.
- Express \(h\) as a function of \(t\). Hence find the amplitude and period of \(h\).
- Sketch the graph of the function in (i) for \(0 \le t \le 30\).
- Find the height of the passenger above the ground after
- \(7.5\) minutes,
- \(15\) minutes, and
- \(20\) minutes.
- Find the interval of time that the passenger is above \(90\) m from the ground.
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Answer:(i) \(h = 90 - 75\cos \left(\dfrac{\pi t}{15}\right)\), amplitude \(75\) m, period \(30\) min; (iii)(a) \(90\) m; (iii)(b) \(165\) m; (iii)(c) \(127.5\) m; (iv) \(7.5 < t < 22.5\)
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