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For the rotation 687^(@), 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 687∘ 687^{\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 687∘ 687^{\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. Check Angle Range: Now, we check if 327327 is between 00 and 360360 degrees.\newline327327 is less than 360360, so it's the coterminal angle we're looking for.
  2. Determine Quadrant: To determine the quadrant, we look at the angle's size.\newlineSince 327327 degrees is more than 270270 but less than 360360, it's in Quadrant IV.
  3. Find Reference Angle: To find the reference angle, we subtract the coterminal angle from 360360 degrees because it's in the fourth quadrant.\newline360−327=33360 - 327 = 33 degrees.

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