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 a 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 and helps in identifying the quadrant in which the terminal side of the angle lies.

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. Understanding these quadrants is essential for determining where an angle's terminal side will fall based on its measure.

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 of the circle. Angles can be expressed in radians or degrees, but in this context, the problem specifies working with radians. Knowing how to interpret and visualize angles in radians is vital for accurately drawing angles and determining their positions in the coordinate system.