Ferris Wheel Problems

Key idea

Height as a sine function of time.

In depth

Height on a wheel follows a sinusoid: h = k + R sin(ωt + φ), with midline = axle height, amplitude = radius, period = time for one revolution. Choose sin or cos according to the starting position.

Worked example

A wheel of radius 10 m, axle 12 m up, 2 min per turn, boarding at the bottom: h = 12 − 10 cos(πt).

Real-world uses

• Calculating a rider’s height at any moment
• Designing fairground and rotating machines

Common mistake

Forgetting the axle height, so heights go below ground.

How to learn this

1. Read the key idea and say it in your own words.
2. Work through the worked example, then try a similar problem.
3. Use the interactive lesson’s visual and mini-quiz to check the pattern.

Frequently asked questions

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Related advanced topics in Trigonometry

• Graph of Tangent – Periodic with vertical asymptotes at odd multiples of π/2.
• Phase Shift – Horizontal translation of a wave.
• Vertical Shift and Midline – Moves the wave up or down.
• General Sinusoid – Combine amplitude, period, phase and shift.
• Graphs of Reciprocal Trig Functions – Secant, cosecant and cotangent graphs.
• Pythagorean Identity – The key identity from the unit circle.