The Unit Circle Clock

Lesson 2 of 11 · 7 min · Free, no account needed

What you will learn

On a circle of radius 1, the point at angle θ is (cos θ, sin θ): across is cos, height is sin.
This works for any angle, not just up to 90°. Left of the center cos is negative, below it sin is negative.
Games draw circles this way: x = cx + r × cos(a), y = cy + r × sin(a).

Your Ferris wheel seat starts at the far right.
The wheel turns 120°. How high are you now, if the radius is 1? Drag the lever to your bet.
Ride the seat around the wheel.
The yellow leg is how far across, the blue leg is how high. Three goals.
Tap every seat that is left of the hub.
Left of the hub means the across number is negative.
Across is cos θ. It is negative when the seat is left of the hub: strictly between 90° and 270°.
This is the unit circle.
A circle of radius 1 around the origin is the unit circle.
The point at angle θ, measured counterclockwise from the right, is (cos θ, sin θ). In a right triangle that matches your ramp ratios, because the hypotenuse is 1.
It also defines cos and sin for any angle. The signs come from the quarter.
Turn the seat onto each target.
Three targets. Then park your own seat and keep it.
Put each angle in its quarter.
The quarter tells you the signs of (cos, sin).
Angles count counterclockwise from the right. Every 90° you pass into the next quarter, and the signs of across and height follow.
Games place things on circles with this code.
cos_deg and sin_deg take degrees. Where does the dot for your seat land? Drag the ghost, then Run.
The seat is at 210°. What is its height?
210° = 180° + 30°. The seat mirrors the 30° seat through the hub, so its height is -sin 30° = -0.5.
Every seat is (cos θ, sin θ).
Speed round: tap the seat for each card. Six in a row.

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