Coterminal Angles Calculator
Results:
Understanding Coterminal Angles
What are Coterminal Angles?
Coterminal angles are angles that share the same terminal side when drawn in standard position. They differ by multiples of 360° (or 2π radians).
θ₁ ≅ θ₂ if θ₁ = θ₂ + 360°n, where n is an integer
θ₁ ≅ θ₂ if θ₁ = θ₂ + 2πn, where n is an integer (in radians)
Common Values Table
| Original Angle | Positive Coterminal | Negative Coterminal | General Form |
|---|---|---|---|
| 30° | 390°, 750° | -330°, -690° | 30° + 360°n |
| π/6 | 13π/6, 25π/6 | -11π/6, -23π/6 | π/6 + 2πn |
| 45° | 405°, 765° | -315°, -675° | 45° + 360°n |
Key Properties
Fundamental Properties
- Infinite number of coterminal angles
- Same trigonometric values
- Same terminal side
- Same reference angle
- Periodic nature
Applications
- Trigonometric functions
- Angular velocity
- Periodic motion
- Wave functions
- Rotational symmetry