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For the rotation 1415^(@), 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 1415∘ 1415^{\circ} , find the coterminal angle from 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 1415∘ 1415^{\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 degrees: To find the coterminal angle between 00 and 360360 degrees, we subtract 360360 degrees from 14151415 degrees until the result is within the desired range.\newline1415−360=10551415 - 360 = 1055\newline1055−360=6951055 - 360 = 695\newline695−360=335695 - 360 = 335
  2. Find coterminal angle: The coterminal angle is 335∘335^\circ.
  3. Identify Quadrant IV: 335335 degrees is in Quadrant IV because it's between 270270 and 360360 degrees.
  4. Find reference angle: To find the reference angle, we subtract the coterminal angle from 360360 degrees because it's in the fourth quadrant.\newline360−335=25360 - 335 = 25

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