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. 90 °

Verified step by step guidance

1. Sketch the angle of 90° in standard position: Start by drawing the initial side along the positive x-axis. Then, rotate counterclockwise to form a 90° angle, which will point directly upwards along the positive y-axis.
2. Draw an arrow to represent the rotation from the initial side to the terminal side, indicating the counterclockwise direction.
3. To find a positive coterminal angle, add 360° to the given angle: 90° + 360°.
4. To find a negative coterminal angle, subtract 360° from the given angle: 90° - 360°.
5. Determine the quadrant: Since 90° lies on the positive y-axis, it is not in any quadrant but is considered to be on the boundary between Quadrant I and Quadrant II.

Key Concepts

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 positioning is crucial for visualizing and sketching angles accurately.

Coterminal Angles

Coterminal angles are angles that share the same terminal side when drawn in standard position, differing by full rotations of 360 degrees. To find coterminal angles, you can add or subtract multiples of 360 degrees from the given angle. For example, for a 90° angle, adding 360° gives 450°, while subtracting 360° results in -270°.

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 and is essential for determining the angle's properties.