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.
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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. This concept is crucial for determining the location of angles in 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 helps in understanding the angle's position.

Radians are a unit of angular measure where one radian is the angle subtended at the center of a circle by an arc equal in length to the radius. The full circle is 2π radians. Understanding radians is essential for working with angles in trigonometry, especially when the problem specifies to work without converting to degrees.