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Overview
Grade 12 Advanced Functions, University Preparation (MHF4U)
B. Trigonometric Functions
21. 12AF.B2.7
21.1 Ferris wheel trig problems
Ferris Wheel Trig Problems
See exactly how a rider's height on a ferris wheel becomes a sine or cosine equation, then practice with fully worked examples.
What You'll Learn
A ferris wheel's height over time is modeled with a sine or cosine function of the form h of t equals A times sine or cosine of B times t plus D
The amplitude A equals the wheel's radius, and the midline D equals the height of the wheel's center above the ground
The period of the function equals the time for one full revolution, which gives the value of B
Whether you use sine or cosine, and whether it is positive or negative, depends on where the rider starts (bottom, top, or side of the wheel)
Once you have the height function, you substitute a time to find height, or set height equal to a value and solve for time
What You'll Practice
1
Graphing height functions for rotating Ferris wheels over time
2
Writing sinusoidal equations from radius, center height, and rotation period
3
Using graphing calculators to find specific heights at given times
4
Finding intersection points to determine time durations above certain heights
Why This Matters
Ferris wheel problems show you how trigonometry models real-world periodic motion. You'll use these same techniques in physics for oscillations, engineering for rotating machinery, and any field involving cyclical patternsfrom tides to sound waves.
Before You Start — Make Sure You Can:
This Unit Includes
1 Video lesson
Learning resources
Skills
Sinusoidal Functions
Periodic Motion
Amplitude
Period
Vertical Shift
Graphing Calculator
Real-World Applications
Trigonometry
ON Curriculum Aligned