Unit Circle Explorer
Drag the point around the circle to see how sin, cos, and tan change. The wave graph on the right traces the function as the angle sweeps.
Controls
Live Values
| θ | 45° (π/4) |
| sin θ | 0.7071 |
| cos θ | 0.7071 |
| tan θ | 1.0000 |
| Quadrant | Q1 |
The Math Behind It
Key Formulas
- On the unit circle: x = cos θ, y = sin θ
- Pythagorean identity: sin²θ + cos²θ = 1
- Tangent: tan θ = sin θ / cos θ
- Period: sin and cos repeat every 2π (360°)
Quadrant Signs
- Q1 (0°-90°): All positive
- Q2 (90°-180°): sin +, cos -, tan -
- Q3 (180°-270°): tan +, sin -, cos -
- Q4 (270°-360°): cos +, sin -, tan -
Special Angles
| θ | rad | sin | cos | tan |
|---|---|---|---|---|
| 0° | 0 | 0 | 1 | 0 |
| 30° | π/6 | 1/2 | √3/2 | 1/√3 |
| 45° | π/4 | √2/2 | √2/2 | 1 |
| 60° | π/3 | √3/2 | 1/2 | √3 |
| 90° | π/2 | 1 | 0 | ∞ |
| 120° | 2π/3 | √3/2 | -1/2 | -√3 |
| 180° | π | 0 | -1 | 0 |
| 270° | 3π/2 | -1 | 0 | ∞ |
Click any row to jump to that angle
You're crushing it!