Reference Angle Calculator

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Switch between degrees and radians. Results are shown in both units either way.
Any positive or negative angle. Values beyond one full revolution are reduced to the equivalent angle in [0, 360°) or [0, 2π) first.
°
Reference AngleQuadrant II
30°

Acute angle (0° to 90°) formed with the nearest x-axis

Reference Angle (radians)0.523599rad
Reduced Angle150°
Quadrant2
sin sign in this quadrantpositive (+)
cos sign in this quadrantnegative (-)
tan sign in this quadrantnegative (-)
30 °
0° - 30°<3030° - 60°30-6060° - 90°60+

Reference angle is 30.0000° in Quadrant II.

  • The terminal side of the angle falls in Quadrant II, so sin is positive (+), cos is negative (-), and tan is negative (-).
  • The reference angle 30.0000° (0.523599 rad) is the acute angle between the terminal side and the nearest x-axis.
  • This is one of the standard angles (0°, 30°, 45°, 60°, 90°), so its trig values can be written as exact fractions without a calculator.

Next stepTo find the actual trig value of the original angle, compute the trig function for the reference angle and apply the sign that matches the quadrant.

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