Question

what rotation about the origin is equivalent to $r_{-500^{circ}}$?\
\\(\bigcirc\\) a. $r_{-280}$\
\\(\bigcirc\\) b. $r_{280}$\
\\(\bigcirc\\) c. $r_{-220}$\
\\(\bigcirc\\) d. $r_{220}$\
reset selection

Explanation:

Step1: Add 360° to reduce angle

$-500^\circ + 360^\circ = -140^\circ$

Step2: Add 360° again to get positive

$-140^\circ + 360^\circ = 220^\circ$

Step3: Verify equivalent rotation

A rotation of $R_{220}$ is equivalent to $R_{-500}$ because rotating $-500^\circ$ (clockwise 500°) is the same as rotating clockwise 500° minus one full 360° rotation, which equals clockwise 140°, or counterclockwise 220°.

Answer:

D. $R_{220}$