For counterclockwise rotations, what value of theta should be used?

In the context of rotation in the Cartesian coordinate system, angles are typically measured from the positive x-axis. A counterclockwise rotation is defined as a movement in the direction opposite to the movement of the hands on a clock. In this convention, counterclockwise angles are represented by positive values.

When you apply a counterclockwise rotation by an angle ( \theta ), you increase the angle positively, meaning that using a positive value of ( \theta ) correctly describes the direction of rotation you want. This is consistent with the standard mathematical definitions used in linear algebra and geometry, where counterclockwise denotes a positive angular direction.

Negative values would indicate clockwise rotations, which is why they do not apply in the case of counterclockwise movements. Zero represents no rotation, and infinity does not pertain to angles in this standard measurement. Therefore, the appropriate angle to use for counterclockwise rotations is indeed a positive value of ( \theta ).