Coterminal Angle Calculator

Find Coterminal Angles with Exact Step-by-Step Solutions

Find the coterminal angle between 0° and 360° (or 0 and 2π) and determine its quadrant. Radians are kept as exact fractions of π.
What are coterminal angles?

Coterminal angles are angles that share the same terminal side. They differ by multiples of 360° (or 2π radians):

\[ \theta_{\text{coterminal}} = \theta + 360° \times k \quad \text{or} \quad \theta_{\text{coterminal}} = \theta + 2\pi k \]

where \(k\) is any integer. This calculator finds the principal coterminal angle in [0°, 360°) or [0, 2π).

Degrees

Coterminal Angle
[0° - 360°)
Quadrant
Step-by-step solution will appear here.

Radians (Exact Fractions)

/ π
Example: 12π/5 = 12/5 π (exact fraction)
Coterminal Angle
[0 - 2π) exact
Quadrant
Step-by-step solution will appear here.

Quadrant Determination

Quadrant I: 0 to π/2 | Quadrant II: π/2 to π
Quadrant III: π to 3π/2 | Quadrant IV: 3π/2 to 2π
Axes: 0, π/2, π, 3π/2, 2π


More References and Links

  • Math Calculators and Solvers
  • Find the Coterminal Angle - analytical tutorial
  • Trigonometry Tutorials