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For the rotation 478^(@), find the coterminal angle from 0^(@) <= theta < 360^(@), the quadrant, and the reference angle. The coterminal angle is ◻^(@), which lies in Quadrant ◻, with a reference angle of ◻^(@).

For the rotation 478∘ 478^{\circ} , find the coterminal angle from 0∘≤θ<360∘ 0^{\circ} \leq \theta<360^{\circ} , the quadrant, and the reference angle.\newlineThe coterminal angle is □∘ \square^{\circ} , which lies in Quadrant □ \square , with a reference angle of □∘ \square^{\circ} .

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Full solution

Q. For the rotation 478∘ 478^{\circ} , find the coterminal angle from 0∘≤θ<360∘ 0^{\circ} \leq \theta<360^{\circ} , the quadrant, and the reference angle.\newlineThe coterminal angle is □∘ \square^{\circ} , which lies in Quadrant □ \square , with a reference angle of □∘ \square^{\circ} .
  1. Determine Quadrant: Now, determine the quadrant where 118118 degrees lies.\newlineSince 118118 degrees is greater than 9090 but less than 180180, it lies in Quadrant II.
  2. Find Reference Angle: To find the reference angle, subtract 118118 degrees from 180180 degrees because the angle is in Quadrant II.\newlineCalculation: 180−118=62180 - 118 = 62 degrees.

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