What are the rules of rotation for specific degrees for both counterclockwise and clockwise?
The rules of rotation for specific degrees, both counterclockwise and clockwise, depend on the context in which the rotation is defined. However, I can provide you with some general guidelines that apply to rotations in a Cartesian coordinate system.
Counterclockwise rotation:
To rotate a point counterclockwise around the origin in a Cartesian coordinate system by a specific angle θ, you can use the following formula:
x' = x * cos(θ) - y * sin(θ)
y' = x * sin(θ) + y * cos(θ)
Here, (x, y) are the coordinates of the point before rotation, and (x', y') are the coordinates of the point after rotation. The angle θ should be given in radians.
Clockwise rotation:
To rotate a point clockwise around the origin by a specific angle θ, you can use the same formula as for counterclockwise rotation. However, this time you need to use the negative of the angle θ:
x' = x * cos(-θ) - y * sin(-θ)
y' = x * sin(-θ) + y * cos(-θ)
It's important to note that the positive direction for angles in a Cartesian coordinate system is counterclockwise. So, if you want to rotate clockwise, you need to use the negative angle.
If you are working with a different coordinate system or need to rotate around a point other than the origin, the formulas may be different. In those cases, you'll need to consult the specific rules or equations for that particular system or situation.