what direction of rotation generates and angle with a measure of -90 degrees? of 120 degrees? what portion of a complete rotation is -90 degrees? 120 degrees?
To determine the direction of rotation that generates an angle with a measure of -90 degrees and 120 degrees, we need to understand the concept of positive and negative angles in mathematics.
In the standard Cartesian coordinate system, angles are measured counterclockwise from the positive x-axis. A positive angle rotates in the counterclockwise direction, while a negative angle rotates in the clockwise direction.
For an angle with a measure of -90 degrees:
To obtain an angle of -90 degrees, we start from the positive x-axis and rotate clockwise by 90 degrees. Therefore, a negative angle of -90 degrees corresponds to a clockwise rotation.
For an angle with a measure of 120 degrees:
To achieve an angle of 120 degrees, we start from the positive x-axis and rotate counterclockwise by 120 degrees. Hence, a positive angle of 120 degrees corresponds to a counterclockwise rotation.
To determine the portion of a complete rotation represented by -90 degrees and 120 degrees:
A complete rotation is equal to 360 degrees. To find the portion of a complete rotation for a given angle, divide the angle measure by 360.
For -90 degrees:
(-90 degrees / 360 degrees) = -1/4 or -0.25
Hence, -90 degrees represents 1/4 or 25% of a complete rotation.
For 120 degrees:
(120 degrees / 360 degrees) = 1/3 or 0.33
Therefore, 120 degrees represents 1/3 or approximately 33% of a complete rotation.