Coterminal Angle Calculator

Your details

Enter any angle, including values greater than 360 or negative angles.
Choose degrees or radians. In radians, enter a decimal value such as 3.1416.
How many positive and how many negative coterminal angles to display.
Principal coterminal angleQuadrant I
45.0000 deg

The equivalent angle in the range [0, 360) or [0, 2pi)

Reference angle45.0000 deg
QuadrantQuadrant I
Positive coterminal angles765.0000 deg, 1125.0000 deg, 1485.0000 deg
Negative coterminal angles45.0000 deg, -315.0000 deg, -675.0000 deg
General formulatheta +- 360*k (k = 1, 2, 3, ...)

Principal angle: 45.0000 deg - Quadrant I

  • The principal coterminal angle is 45.0000 deg, which is the unique equivalent angle in the standard range.
  • The reference angle is 45.0000 deg, the acute angle between the terminal side and the nearest part of the x-axis.
  • The terminal side of the angle lies in Quadrant I.
  • Your input of 405 degrees represents 1.13 full rotations from the start position.

Next stepCoterminal angles share the same terminal side, so they have identical sine, cosine and tangent values. Use coterminal reduction before evaluating any trig function of a large angle.

 = Powered by OnlyCalculators