The Ferris wheel seat
Ride a Ferris wheel and your height rises, peaks, falls, and repeats in a smooth wave. Plot that height against time and you've drawn a sine curve — trigonometry describes anything that cycles round and round.
Going around the circle
On the unit circle, the sine of an angle is the height (y-coordinate) and cosine is the horizontal position (x-coordinate). As the angle increases, the height traces out the smooth, repeating sine wave.
Simulation · Wave: amplitude & frequency
This is the shape of sine: change the frequency to change the period, and the amplitude to change its height.
Lab · Sine at key angles
- At 0°, the height on the unit circle is 0 — so sin(0) = 0.
- At 90°, the point is at the top — so sin(90°) = 1.
- Picture the wave rising from 0 up to 1.
What you should see: sin(0°) = 0 and sin(90°) = 1 — the wave rises from zero to its peak of 1.