Height on a Ferris Wheel

Trigonometry · Axiom Academy

LESSON Ferris Wheel: Sine and Cosine Experience how circular motion creates sine and cosine waves—the foundation of trigonometry! Imagine riding a Ferris wheel at the carnival. As you rotate around the center, your height above the ground and your horizontal distance from center follow predictable patterns—patterns described by sine and cosine! As the wheel spins, your vertical position traces a sine wave and your horizontal position traces a cosine wave ! Now it's your turn! Adjust the rotation speed and starting position to see how sine and cosine change. You've seen how sine represents vertical position and cosine represents horizontal position. Now let's discover an important relationship! Let's visualize how sine and cosine create waves as the Ferris wheel completes a full rotation! Starts at 0 when θ = 0° Maximum at 90° (top of wheel) Returns to 0 at 180° Starts at 1 when θ = 0° Zero at 90° (directly above center) Minimum at 180° Key Insight: Cosine is just sine shifted by 90°! cos(θ) = sin(θ + 90°) Circular Motion Creates Waves As you rotate, your vertical and horizontal positions oscillate in sine and cosine patterns Sine = Vertical Position sin(θ) tells you how high you are relative to the center ↔ Cosine = Horizontal Position cos(θ) tells you how far left or right you are from center Phase Shift Connection Sine and cosine are the same wave, just 90° out of phase Everywhere in Nature Sound waves, light waves, pendulums, and tides all follow these patterns!

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