Trigonometry — Directed Angle

About this lesson

This unit introduces the concept of directed angles, which are ordered pairs of rays sharing a common vertex, distinguishing between initial and terminal sides. It explains the standard position of an angle (vertex at the origin, initial side on the positive x-axis) and how to determine if an angle is in standard position. The unit covers positive and negative measures of directed angles based on rotation direction (anticlockwise positive, clockwise negative), and how to find the equivalent positive or negative measure by adding or subtracting 360°. It also defines quadrantal angles (terminal side on an axis) and how to determine the quadrant in which an angle lies based on its measure. Equivalent angles (coterminal angles) are introduced as angles that share the same terminal side, differing by multiples of 360°. The unit includes worked examples and exercises for finding positive and negative measures, determining quadrants, and identifying equivalent angles.