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For the rotation 417^(@), 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 417∘ 417^{\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 417∘ 417^{\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. Subtract 360360°: To find the coterminal angle between 0°0° and 360°360°, subtract 360°360° from 417°417° until the result is within the desired range.\newline417°−360°=57°417° - 360° = 57°
  2. Check Range: The coterminal angle is 57∘57^\circ, which is between 0∘0^\circ and 360∘360^\circ.
  3. Identify Quadrant: 57°57° lies in Quadrant I because it's between 0°0° and 90°90°.
  4. Find Reference Angle: The reference angle for an angle in Quadrant I is the angle itself.\newlineReference angle = 57∘57^\circ

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