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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