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For the rotation -1053^(@), 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 −1053∘ -1053^{\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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Q. For the rotation −1053∘ -1053^{\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. Add 360360°: To find the coterminal angle, add or subtract multiples of 360°360° until the angle is between 0°0° and 360°360°.\newline−1053°+360°=−693°-1053° + 360° = -693°
  2. Keep adding 360360°: Keep adding 360360° until the angle is positive.\newline−693°+360°=−333°-693° + 360° = -333°
  3. Add 360360°: Add 360360° again.\newline−333°+360°=27°-333° + 360° = 27°\newlineNow, 27°27° is between 0°0° and 360°360°, so it's the coterminal angle we're looking for.
  4. Identify Quadrant: The coterminal angle 27°27° lies in Quadrant I because it's between 0°0° and 90°90°.
  5. Find Reference Angle: The reference angle is the acute angle formed by the terminal side of the angle and the x-axis. Since 27∘27^\circ is already in Quadrant I and is acute, the reference angle is the same as the coterminal angle: 27∘27^\circ.

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