Kung Fu Math · kungfumath.app
The unit circle
A point on the unit circle has coordinates (cos θ, sin θ). Start with the first quadrant, then use symmetry to find the signs.
Exact values · first quadrant
- θ · radians · cos θ · sin θ · tan θ
- 0° · 0 · 1 · 0 · 0
- 30° · π/6 · √3/2 · 1/2 · √3/3
- 45° · π/4 · √2/2 · √2/2 · 1
- 60° · π/3 · 1/2 · √3/2 · √3
- 90° · π/2 · 0 · 1 · undefined
Signs & symmetry
- I: cos +, sin +, tan +
- II: cos −, sin +, tan −
- III: cos −, sin −, tan +
- IV: cos +, sin −, tan −
- sin(−θ) = −sin θ; cos(−θ) = cos θ
- sin² θ + cos² θ = 1; tan θ = sin θ / cos θ
Degrees ↔ radians
- radians = degrees × π/180
- degrees = radians × 180/π
- 180° = π; 270° = 3π/2; 360° = 2π
- Example: sin 150° = sin 30° = 1/2
- tan θ is undefined when cos θ = 0.
Kung Fu Math · unit-circle · kungfumath.app/cheat-sheets