Work out reference angle instantly with clear inputs, formula shown and shareable results.
The reference angle is the acute angle between the terminal arm and the x-axis. It is found by reducing the angle to 0°–360° and then subtracting from or to the nearest multiple of 180°, which lets you read trig values off the first quadrant.
By quadrant
Q1: θ, Q2: 180° − θ, Q3: θ − 180°, Q4: 360° − θ
210° is in quadrant 3, so the reference angle is 210 − 180 = 30°.
sin 210° = −sin 30° = −0.5. The reference angle gives the magnitude and the quadrant gives the sign.