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For the rotation 670^(@), 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 670∘ 670^{\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 670∘ 670^{\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, subtract 360360 degrees until the angle is between 00 and 360360 degrees.\newline670−360=310670 - 360 = 310
  2. Check range: Check if 310310 is between 00 and 360360 degrees.\newlineYes, it is.
  3. Determine quadrant: Determine the quadrant for 310310 degrees.\newlineSince 310310 is between 270270 and 360360, it's in Quadrant IV.
  4. Find reference angle: Find the reference angle by subtracting 310310 from 360360. \newline360−310=50 degrees.360 - 310 = 50 \text{ degrees}.

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