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For the rotation 708^(@), 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 708∘ 708^{\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 708∘ 708^{\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 from 708708: To find the coterminal angle between 00 and 360360 degrees, subtract multiples of 360360 from 708708 until the result is within the desired range.\newlineCalculation: 708−360=348708 - 360 = 348.
  2. Identify coterminal angle: Since 348348 is less than 360360 and greater than 00, it is the coterminal angle we are looking for.
  3. Determine quadrant: To determine the quadrant, observe that 348348 degrees is between 270270 and 360360 degrees, which places it in Quadrant IV.
  4. Find reference angle: To find the reference angle, subtract the coterminal angle from 360360 degrees.\newlineCalculation: 360−348=12360 - 348 = 12 degrees.

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