Trigonometry begins with angles and right triangles, then expands to the unit circle: every angle places a point (cos θ, sin θ) on a circle of radius 1.
You can control the angle with the slider (keyboard-friendly), preset buttons, or by dragging on the diagrams.
Unit circle
Try it: Use the angle slider or Tab to the presets. Cosine is the horizontal dashed leg; sine is the vertical one. Drag is optional.
What the diagram is showing
- Point on the circle — position at angle θ
- Horizontal dashed leg — cosine (x-coordinate)
- Vertical dashed leg — sine (y-coordinate)
- Arc — measure of θ from the positive x-axis
Meaning is not color-only: position, dash style, and the numeric readout all convey the same information.
From circle to wave
The height of the point is sin θ. The wave below plots that height against θ. Use the same slider—wave and circle stay linked.
Sine wave linked to the same angle
The vertical line marks θ. The marker height is sin θ. Change θ with the slider above (or drag on the wave).
Check: Set θ to 90° with the preset. Cosine ≈ 0, sine ≈ 1—point at the top; wave marker at the first peak.
Practice — Standard → Trigonometry
Open Hyper-Scale Lab