Find the Quadrant of the Angle 225 degrees

Problem

225^∘

Solution

1. Identify the standard ranges for each quadrant in a coordinate system where 0^∘≤θ<360^∘

2. Recall that Quadrant I is 0^∘<θ<90^∘ Quadrant II is 90^∘<θ<180^∘ Quadrant III is 180^∘<θ<270^∘ and Quadrant IV is 270^∘<θ<360^∘

3. Compare the given angle 225^∘ to these ranges.

4. Determine that since 180^∘<225^∘<270^∘ the angle lies in the third quadrant.

Final Answer

Quadrant of *225^∘=Quadrant III

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