Question

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. ―61 °

Accepted Answer

Start by understanding that an angle in standard position has its vertex at the origin and its initial side along the positive x-axis. The angle is measured by rotating the initial side either counterclockwise for positive angles or clockwise for negative angles. Since the given angle is -61°, this means you rotate 61° clockwise from the positive x-axis. Sketch this by drawing the initial side along the positive x-axis and then an arrow rotating clockwise 61° to represent the terminal side. To find a positive coterminal angle, add 360° to the given angle: $$-61° + 360° = 299°. $$This angle represents a counterclockwise rotation from the positive x-axis and ends at the same terminal side as -61°. To find a negative coterminal angle, subtract 360° from the given angle: $$-61° - 360° = -421°. $$This represents a clockwise rotation that also ends at the same terminal side. Determine the quadrant for each angle by considering their measures: -61° lies in Quadrant IV (since it is between 0° and -90°), 299° lies in Quadrant IV (since it is between 270° and 360°), and -421° can be simplified by adding 360° to find its equivalent positive angle, which will also place it in Quadrant IV.

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. ―61 °

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Standard Position of an Angle

Coterminal Angles

Quadrants and Angle Location