Look up exact sin, cos, tan values and coordinates for standard unit-circle angles.
The unit circle is a circle of radius 1 centred at the origin. Any angle θ maps to the point (cos θ, sin θ). The reference angle is the acute angle formed with the x-axis; the quadrant determines the sign of each function.
Unit circle coordinates
(x, y) = (cos θ, sin θ) on a circle of radius 1
0°, 30°, 45°, 60°, 90° and their counterparts in each quadrant: 120°, 135°, 150°, 180°, 210°, 225°, 240°, 270°, 300°, 315°, 330°, 360°.
In Q1: ref = θ; in Q2: ref = 180° − θ; in Q3: ref = θ − 180°; in Q4: ref = 360° − θ.