Reference angle calculator

Find the reference angle — the acute angle between the terminal side and the x-axis. Always between 0° and 90°.

Angle°

Reference angle rules

Q1 (0°–90°): ref = θ. Q2 (90°–180°): ref = 180° − θ. Q3 (180°–270°): ref = θ − 180°. Q4 (270°–360°): ref = 360° − θ.

Reference angle of 150° = 180° − 150° = 30°. So sin(150°) = sin(30°) = ½.

Why it matters

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

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