b) Which of the points below is equivalent to \( \left(2,120^{\circ}\right) \) ? Select all that apply. \( \square \) A. \( \left(-2,480^{\circ}\right) \) \( \square \) B. \( \left(-2,300^{\circ}\right) \) \( \square \) C. \( \left(-2,120^{\circ}\right) \) \( \square \) D. \( \left(2,480^{\circ}\right) \)
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To find points equivalent to \( \left(2,120^{\circ}\right) \), we must look for points that have the same angle (modulo 360°) and same distance from the origin. Since \( 120^{\circ} \) is the same as \( 120^{\circ} + 360^{\circ}k \) for integer \( k \), we can manipulate the angles to find equivalents. - For \( A \): The angle \( 480^{\circ} - 360^{\circ} = 120^{\circ} \), so \( \left(-2,480^{\circ}\right) \) is equivalent. - For \( B \): The angle \( 300^{\circ} \) does not equal \( 120^{\circ} \) or any rotations thereof, so it is not equivalent. - For \( C \): The angle \( -120^{\circ} \) can be rewritten as \( 120^{\circ} + 360^{\circ}(-1) = 240^{\circ} \), which does not match \( 120^{\circ} \). Thus, it is not equivalent. - For \( D \): The angle \( 480^{\circ} \), as calculated before, corresponds to \( 120^{\circ} \). Thus, \( \left(2,480^{\circ}\right) \) is equivalent. In conclusion, the equivalent points are \( A \) and \( D \).