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 °

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Step 1: Begin by sketching the angle -61° in standard position. Start from the positive x-axis and rotate clockwise since the angle is negative.

Step 2: Draw an arrow to represent the rotation of -61° from the positive x-axis. This angle will end in the fourth quadrant.

Step 3: To find a positive coterminal angle, add 360° to -61°. This will give you an angle that is coterminal and positive.

Step 4: To find a negative coterminal angle, subtract 360° from -61°. This will give you another angle that is coterminal and negative.

Step 5: Identify the quadrant for each angle: -61° is in the fourth quadrant, the positive coterminal angle will also be in the fourth quadrant, and the negative coterminal angle will be in the same quadrant as -61°.

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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 system and its initial side lies along the positive x-axis. The angle is measured from the initial side to the terminal side, with positive angles measured counterclockwise and negative angles measured clockwise. Understanding this concept is crucial for sketching angles accurately.

Coterminal Angles

Coterminal angles are angles that share the same terminal side when drawn in standard position. To find coterminal angles, you can add or subtract multiples of 360 degrees (or 2π radians). For example, for an angle of -61°, adding 360° gives a positive coterminal angle of 299°.

Quadrants of the Coordinate Plane

The coordinate plane is divided into four quadrants, each defined by the signs of the x and y coordinates. Quadrant I has both coordinates positive, Quadrant II has a negative x and positive y, Quadrant III has both negative, and Quadrant IV has a positive x and negative y. Identifying the quadrant of an angle helps in understanding its position relative to the axes.

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