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For the rotation 1036^(@), 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 1036∘ 1036^{\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 1036∘ 1036^{\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, subtract multiples of 360360 from 10361036 until the result is within the desired range.\newline1036−360=6761036 - 360 = 676
  2. Check Within Range: Continue subtracting 360360 degrees: 676−360=316676 - 360 = 316 Now, 316316 degrees is within the range of 00 to 360360 degrees.
  3. Determine Quadrant: To determine the quadrant, note that angles between 270270 and 360360 degrees lie in Quadrant IV.\newline316316 degrees is between 270270 and 360360 degrees.
  4. Find Reference Angle: The reference angle is the acute angle formed by the terminal side of the angle and the x-axis. For angles in Quadrant IV, subtract the angle from 360360 degrees.\newline360−316=44360 - 316 = 44 degrees

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