The least positive coterminal angle is \( 482^{\circ} \). (Simplify your answer. Type an integer or a fraction.) The greatest negative coterminal angle is \( -238^{\circ} \). (Simplify your answer. Type an integer or a fraction.) When it is in standard position, the terminal side of A lies in

Let's simplify the given coterminal angles and determine the quadrant in which the terminal side of angle \( A \) lies when it's in standard position. ### 1. Least Positive Coterminal Angle for \( 482^{\circ} \) To find the least positive coterminal angle, subtract \( 360^{\circ} \) from \( 482^{\circ} \): \[ 482^{\circ} - 360^{\circ} = 122^{\circ} \] **Simplified Answer:** \( \boxed{122} \) ### 2. Greatest Negative Coterminal Angle for \( -238^{\circ} \) To find the greatest negative coterminal angle, we want the coterminal angle that's closest to \( 0^{\circ} \) but still negative. Since adding \( 360^{\circ} \) to \( -238^{\circ} \) gives a positive angle: \[ -238^{\circ} + 360^{\circ} = 122^{\circ} \] This is positive, so the greatest negative coterminal angle is the original angle itself. **Simplified Answer:** \( \boxed{-238} \) ### 3. Quadrant of Angle \( A \) in Standard Position The least positive coterminal angle is \( 122^{\circ} \). To determine the quadrant: - **Quadrant I:** \( 0^{\circ} < \theta < 90^{\circ} \) - **Quadrant II:** \( 90^{\circ} < \theta < 180^{\circ} \) - **Quadrant III:** \( 180^{\circ} < \theta < 270^{\circ} \) - **Quadrant IV:** \( 270^{\circ} < \theta < 360^{\circ} \) Since \( 122^{\circ} \) is between \( 90^{\circ} \) and \( 180^{\circ} \), the terminal side of angle \( A \) lies in: **Answer:** **Quadrant II**