In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.
-210°

Key Concepts

Standard Position of Angles

An angle is said to be in standard position when its vertex is at the origin of a coordinate system and its initial side lies along the positive x-axis. The angle is measured counterclockwise from the initial side. If the angle is negative, it is measured clockwise. Understanding this concept is crucial for accurately determining the location of angles in the coordinate plane.

Quadrants of the Coordinate Plane

The coordinate plane is divided into four quadrants, each defined by the signs of the x and y coordinates. Quadrant I has positive x and y values, Quadrant II has negative x and positive y, Quadrant III has negative x and y, and Quadrant IV has positive x and negative y. Identifying the quadrant in which an angle lies helps in understanding its properties and the signs of trigonometric functions associated with that angle.

Angle Measurement in Radians and Degrees

Angles can be measured in degrees or radians, with one full rotation (360 degrees) equivalent to 2π radians. In this context, the angle of -210° can be analyzed without converting to radians, as the negative sign indicates a clockwise rotation. Recognizing the relationship between these two measurement systems is essential for solving problems involving angles in trigonometry.