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Ride a Ferris Wheel

Part of the Graphs of Trig Functions section of Coddy's Trigonometry journey. Lesson 1 of 51.

A Ferris wheel of radius 3 m turns anticlockwise. Your seat starts level with the hub, on the side that is about to rise. After the wheel turns through an angle θ, your height above the hub is 3sin(theta) metres: 3 m above it at 90°, level with it at 180°, 3 m below it at 270°.

$A wheel of radius 3 with a seat turned through θ and its height h above the hub$

Plot that height against the angle and the dots join into a wave. One turn of 360° draws one full wave. The next turn draws the same wave again, because the seat passes the same heights in the same order.

$The height wave of a wheel of radius 3: top 3 at 90 degrees, bottom -3 at 270 degrees$

On the graph board the wave starts as the ride on a wheel of radius 1. Drag its highest dot to set how high the seat goes.

Challenge

A smaller wheel has radius 2 m. Your seat starts level with the hub and rises first. Draw your height above the hub, in metres, against the angle the wheel has turned. Press Check.

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Graphs of Trig Functions

1From Circle to Wave

Ride a Ferris WheelHeight on the Unit Circle Unrolling the Sine Graph The Sine Graph in Radians Circle to Wave Recap

4Period

Period: One Wave Long Stretching the Wave Period in Degrees b Is Not the Period Period Recap

7Reading a Graph

The Equation of a Wave Sine or Cosine?From Peaks to a Wave All Four at Once Reading Recap

10Final Challenges

A Wave From Its Facts A Hidden Shift A Flipped Tangent Read the Whole Wave Giant Wheel: the Model Giant Wheel: the Height

2The Cosine Graph

Cosine: the Point's x The Cosine Graph Cosine Is a Shifted Sine Where Sine Meets Cosine Cosine Graph Recap

5Midline

The Midline From Highest and Lowest Reading the Midline Midline Recap

8The Tangent Graph

The Tangent Graph Asymptotes Stretching the Tangent Graphs of sec, csc and cot Tangent Recap

3Amplitude

Amplitude: How Tall Amplitude of a Cosine A Negative a Flips It Amplitude From a Graph Amplitude Recap

6Phase Shift

Phase Shift: Sliding Phase Shift in Degrees Factor Out b First Reading a Phase Shift Phase Shift Recap

9Modelling with Waves

A Ferris Wheel Model Daylight Over a Year Tides Using a Model A Spring's Bounce Modelling Recap