Concept Check Sketch each angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, that are coterminal with the given angle. Give the quadrant of each angle, if applicable. 300 °

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Start by sketching the angle of \(300^\circ\) in standard position. This means drawing an initial side along the positive x-axis and rotating counterclockwise by \(300^\circ\) to locate the terminal side of the angle.

Draw an arrow from the initial side to the terminal side to represent the \(300^\circ\) rotation. Since \(300^\circ\) is more than \(270^\circ\) but less than \(360^\circ\), the terminal side will lie in the fourth quadrant.

To find a positive coterminal angle, add \(360^\circ\) to \(300^\circ\): \(300^\circ + 360^\circ = 660^\circ\). This angle shares the same terminal side and is also in the fourth quadrant.

To find a negative coterminal angle, subtract \(360^\circ\) from \(300^\circ\): \(300^\circ - 360^\circ = -60^\circ\). This angle rotates clockwise from the initial side and also ends in the fourth quadrant.

Identify the quadrant for each angle: the original \(300^\circ\), the positive coterminal \(660^\circ\), and the negative coterminal \(-60^\circ\) all terminate in the fourth quadrant.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Standard Position of an Angle

An angle is in standard position when its vertex is at the origin of a coordinate plane and its initial side lies along the positive x-axis. The angle is measured by rotating the initial side to the terminal side, either counterclockwise for positive angles or clockwise for negative angles.

Coterminal Angles

Coterminal angles share the same terminal side but differ by full rotations of 360°. To find coterminal angles, add or subtract multiples of 360° from the given angle. This helps identify equivalent angles in different rotations.

Quadrants and Angle Location

The coordinate plane is divided into four quadrants, each corresponding to a range of angle measures: Quadrant I (0° to 90°), II (90° to 180°), III (180° to 270°), and IV (270° to 360°). Determining the quadrant of an angle helps understand the sign of trigonometric functions and the angle's position.