The Amazing Unit Circle Nice Angles in Degrees Angles are measured in standard position from the positive horizontal axis going counter-clockwise (for the positive direction). One whole revolution is 360°. The circle is then divided up to find other nice angles. Half a revolution is therefore equal to 360°/2 = 180°. One quarter of a revolution (a right angle) equals 360°/4 = 90°. Three quarters of a revolution measures 3 × 90° = 270°. One eighth of a revolution is the angle that divides the first quadrant in half; it is half a right angle: 360°/8 = 90°/2 = 45°. The angles that bisect the other quadrants are 90° + 45° = 135°, 180° + 45° = 225° and 270° + 45° = 315°. The angle one third of the way through the first quadrant is one twelfth of a revolution, that is, 90°/3 = 360°/12 = 30°. Double 30° is two-thirds of the way through the first quadrant, or one sixth of a revolution: 2 × 30° = 360°/6 = 60°. The angles one third and two thirds of the way through the second, third and fourth quadrants are 90° + 30° = 120°, 90° + 60° = 150°, 180° + 30° = 210°, 180° + 60° = 240°, 270° + 30° = 300° and 270° + 60° = 330°. Finally, let's not forget the angle with measure 0°. In increasing order: 0°, 30°, 45°, 60°, 90°, 120°, 135°, 150°, 180°, 210°, 225°, 240°, 270°, 300°, 315°, 330°, 360°. These are the "nice" angles. Of course, you can continue to subdivide one revolution to locate any angle you wish. Angles with measure greater than 360° complete one or more complete revolution(s) plus the remainder left when dividing the angle measure by 360. Angles with negative measure are taken in the clockwise direction. The Amazing Unit Circle | Trigonometry Facts | Home Page | Privacy Policy