Final answer:
To find an equivalent rotation for R-500°, we subtract 360° from -500° to obtain R-140°, which is within the standard range of 0° to 360°.
Step-by-step explanation:
When discussing rotation about the origin, we must consider that a complete rotation is 360 degrees. Rotations beyond a full rotation can be simplified removing full rotations out of them.
In this case, we want to find a rotation equivalent to R-500°, which means a rotation 500 degrees in the counterclockwise direction.
To find an equivalent rotation within a 0° to 360° range, we can add or subtract 360° until we reach a value in that range. Subtracting 360° from -500° gives us R-140°, which is the equivalent rotation within the 0° to 360° range.
Thus, the equivalent rotation about the origin to R-500° is R-140°.