Special right triangle allows one to quickly calculate various lengths in geometric problems without resorting to more advanced methods. "Angle-based" special right triangles are specified by the relationships of the angles of which the triangle is composed. The angles of these triangles are such that the larger (right) angle, which is 90 degrees or radians, is equal to the sum of the other two angles. The side lengths are generally deduced from the basis of the unit circle or other geometric methods. This approach may be used to rapidly reproduce the values of trigonometric functions for the angles 30°, 45°, and 60°. Special
Angle or "terminal side" is defined by the measure from the initial side in radians, degrees, or turns. With "positive angles" representing rotations toward the positive y-axis and "negative angles" representing rotations toward the negative "y"-axis. When Cartesian coordinates are represented by "standard position", defined by the "x"-axis rightward and the "y"-axis upward, positive rotations are anticlockwise and negative rotations are clockwise. In many contexts, an angle of −"θ" is effectively equivalent to an angle of "one full turn minus "θ"". For example, an orientation represented as −45° is effectively equivalent to an orientation represented as 360° − 45° or 315°.