Find the Quadrant of the Angle -225 degrees

Problem

−225^∘

Solution

1. Find a coterminal angle by adding 360^∘ to the given negative angle to find its equivalent position between 0^∘ and 360^∘

−225^∘+360^∘=135^∘

2. Identify the quadrant boundaries in the standard coordinate system where 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 angle to the boundaries. Since 135^∘ is greater than 90^∘ and less than 180^∘ it lies in the second quadrant.

90^∘<135^∘<180^∘

Final Answer

Quadrant of −225^∘=Quadrant II

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