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°

검증된 단계별 안내

Understand that the angle is measured in standard position, meaning its vertex is at the origin and the initial side lies along the positive x-axis.

Since the angle is 120°, start from the positive x-axis and rotate counterclockwise by 120°.

Locate 120° on the circle: it is between 90° and 180°, which places the terminal side of the angle in the second quadrant.

Draw the terminal side of the angle so that it forms a 120° rotation from the positive x-axis, intersecting the circle in the second quadrant.

State that the angle lies in the second quadrant because 120° is greater than 90° but less than 180°.

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주요 개념

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Angles in Standard Position

An angle is 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 terminal side is determined by rotating the initial side counterclockwise for positive angles and clockwise for negative angles.

Quadrants of the Coordinate Plane

The coordinate plane is divided into four quadrants by the x- and y-axes. 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. The quadrant of an angle depends on the location of its terminal side.

Measuring Angles in Degrees and Radians

Angles can be measured in degrees or radians. Degrees divide a circle into 360 parts, while radians relate the angle to the radius of the circle. For this problem, angles are given in degrees (e.g., 120°), and the task is to identify the quadrant without converting to radians.

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°