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 °

Verified step by step guidance

1. 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.
2. 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.
3. 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°.
4. 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.
5. 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.

Key Concepts

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°). Knowing the quadrant helps determine the sign of trigonometric functions and the angle's position.