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.
120°

Key Concepts

Standard Position of an Angle

An angle is said to be in standard position when its vertex is at the origin of the coordinate system and its initial side lies along the positive x-axis. The angle is measured counterclockwise from the initial side. For example, a 120° angle starts from the positive x-axis and rotates counterclockwise, landing in the second quadrant.

Quadrants of the Coordinate System

The rectangular coordinate system is divided into four quadrants. Quadrant I is where both x and y are positive, Quadrant II has a negative x and positive y, Quadrant III has both negative x and y, and Quadrant IV has a positive x and negative y. Understanding which quadrant an angle lies in helps determine the signs of the trigonometric functions associated with that angle.

Angle Measurement in Radians and Degrees

Angles can be measured in degrees or radians. One complete revolution (360°) is equivalent to 2π radians. To convert degrees to radians, multiply by π/180. In this exercise, the angle is given in degrees (120°), but it can be analyzed in radians without conversion, as the focus is on its position and quadrant rather than its exact trigonometric values.