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For the rotation 804^(@), 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 804∘ 804^{\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 804∘ 804^{\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 804804: To find the coterminal angle between 00 and 360360 degrees, subtract 360360 degrees from 804804 degrees until the result is within the desired range.\newline804−360=444804 - 360 = 444 degrees.
  2. Subtract 360360 again: Subtract 360360 degrees again because 444444 is still greater than 360360. \newline444−360=84444 - 360 = 84 degrees.
  3. Identify coterminal angle quadrant: The coterminal angle is 84∘84^\circ, which is between 00 and 90∘90^\circ, so it lies in Quadrant I.
  4. Determine reference angle: Since 8484 degrees is in Quadrant I, the reference angle is the same as the coterminal angle, which is 8484 degrees.

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