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. If the angle measures more than 360 degrees or 2π radians, it can be reduced to an equivalent angle within the range of 0 to 2π by subtracting full rotations.

The rectangular coordinate system is divided into four quadrants based on the signs of the x and y coordinates. Quadrant I contains 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 which quadrant an angle lies in helps determine the signs of the trigonometric functions associated with that angle.

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. The full circle is 2π radians, which is equivalent to 360 degrees. When working with angles in radians, it is essential to understand how to visualize and interpret these angles on the unit circle, especially when determining their position and corresponding quadrant.