Reference and Coterminal Angle Calculator
Reference and Coterminal Angle Calculator
Enter any angle, positive or negative, larger or smaller than a full circle, to find its coterminal angle (the equivalent angle within one full 360° rotation) and its reference angle (the acute angle formed with the x-axis) — both fundamental for trigonometry problems.
A coterminal angle is found by repeatedly adding or subtracting 360° until the result lands within the standard [0°, 360°) range — 740° reduces to 20° (740 minus two full rotations of 360°), since both angles point in exactly the same direction on a circle despite the raw number looking very different. The reference angle, always between 0° and 90°, measures the acute angle formed between the terminal side and the nearest x-axis, and it's the key that unlocks evaluating trig functions for angles outside the first quadrant using only the familiar first-quadrant values.
- Coterminal angle: found by adding or subtracting 360° until the result falls in [0°, 360°).
- Reference angle: always between 0° and 90°, measured from the terminal side of the angle to the nearest x-axis.
- Example: 740° has a coterminal angle of 20° (740 − 2×360 = 20°) and a reference angle of 20° (since it's already in quadrant 1).
What is the reference angle for 200°?
200° is in quadrant 3, so the reference angle is 200° − 180° = 20°.
What about negative angles like -30°?
The coterminal angle is 330° (-30° + 360°), which is in quadrant 4, giving a reference angle of 360° − 330° = 30°.
Reference and Coterminal Angle Calculator
Enter any angle, positive or negative, larger or smaller than a full circle, to find its coterminal angle (the equivalent angle within one full 360° rotation) and its reference angle (the acute angle formed with the x-axis) — both fundamental for trigonometry problems.
A coterminal angle is found by repeatedly adding or subtracting 360° until the result lands within the standard [0°, 360°) range — 740° reduces to 20° (740 minus two full rotations of 360°), since both angles point in exactly the same direction on a circle despite the raw number looking very different. The reference angle, always between 0° and 90°, measures the acute angle formed between the terminal side and the nearest x-axis, and it's the key that unlocks evaluating trig functions for angles outside the first quadrant using only the familiar first-quadrant values.
- Coterminal angle: found by adding or subtracting 360° until the result falls in [0°, 360°).
- Reference angle: always between 0° and 90°, measured from the terminal side of the angle to the nearest x-axis.
- Example: 740° has a coterminal angle of 20° (740 − 2×360 = 20°) and a reference angle of 20° (since it's already in quadrant 1).
What is the reference angle for 200°?
200° is in quadrant 3, so the reference angle is 200° − 180° = 20°.
What about negative angles like -30°?
The coterminal angle is 330° (-30° + 360°), which is in quadrant 4, giving a reference angle of 360° − 330° = 30°.