What is the appropriate value of theta for clockwise rotations?

In the context of rotations in a coordinate plane, counterclockwise rotations are conventionally represented by positive angles, while clockwise rotations are represented by negative angles. This convention arises from the way angles are measured in mathematics, starting from the positive x-axis.

When you move in a clockwise direction from the positive x-axis, the angle decreases; thus, it is represented as a negative value. Therefore, for executing rotations in a clockwise manner, theta should indeed be a negative value. This reflects the standard mathematical practice where negative angles denote a clockwise direction.

In contrast, positive and zero values for theta do not correspond to clockwise rotations, and mathematically undefined does not apply in this context since angles can indeed be defined as negative for clockwise rotations.