The model for the height of a passenger on a Ferris wheel is

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

The model for the height of a passenger on a Ferris wheel is h(t)=20−19cos⁡2πt3h(t)=20-19\cos\frac{2\pi t}{3}, where hh is the height in metres above the ground and tt is in minutes. (1) Where is the passenger at time t=0t=0? (2) At what time is the passenger at the maximum height in the first revolution of the wheel? (3) How long does the wheel take to complete one revolution? (4) Sketch the graph of the function h(t)h(t) over one revolution. (5) The passenger can see their friend when they are at least 13 m13\text{ m} above the ground. During what times in the first revolution can the passenger see their friend?

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