Home›Math›Reference Angle

Reference Angle Calculator

The acute angle (0° to 90°) formed between the terminal side of an angle and the x-axis. It helps find trig values for any angle.

Trig functions of any angle equal ± the trig function of its reference angle. The sign depends on the quadrant (ASTC rule).

All trig functions positive in Q1, Sine in Q2, Tangent in Q3, Cosine in Q4.

Find the reference angle and quadrant for any angle. The reference angle is the acute angle formed with the x-axis.

Calculator

Unit

DegreesRadians

Angle (°)

The reference angle is always acute (0° to 90°) and is measured to the nearest x-axis.

Quadrant I

ref = θ

0° < θ < 90°

Quadrant II

ref = 180° - θ

90° < θ < 180°

Quadrant III

ref = θ - 180°

180° < θ < 270°

Quadrant IV

ref = 360° - θ

270° < θ < 360°

The acute angle (0° to 90°) formed between the terminal side of an angle and the x-axis. It helps find trig values for any angle.

Trig functions of any angle equal ± the trig function of its reference angle. The sign depends on the quadrant (ASTC rule).

All trig functions positive in Q1, Sine in Q2, Tangent in Q3, Cosine in Q4.

Please wait a moment