Final answer:
The rotation rule describes the rotation about the origin in mathematics. The new coordinates of a point (x, y) after rotation can be determined using trigonometric functions. The angle of rotation can be calculated using the arc length formula.
Step-by-step explanation:
In mathematics, the rule that describes rotation about the origin is referred to as the rotation rule or the radian rule. When a point (x, y) is rotated about the origin, the new coordinates (x', y') can be determined using the following formulas:
x' = x * cos(theta) - y * sin(theta)
y' = x * sin(theta) + y * cos(theta)
The angle of rotation can be calculated using the arc length formula:
Angle = (Arc Length / Circle Circumference) * 360 degrees
For example, if the arc length separating the two hands of a clock is 1.0 meter and the radius of the clock is 0.70 meters, the angle of rotation can be calculated as follows:
Angle = (1.0 / (2 * pi * 0.70)) * 360 = 81 degrees