Find the Quadrant of the Angle -(3pi)/4

Problem

−(3*π)/4

Solution

1. Convert to degrees to visualize the angle more easily.

θ=−(3*π)/4⋅180^∘/π

θ=−135^∘

2. Find the coterminal angle by adding 360^∘ (or 2*π radians) to the negative angle to find its position within the standard 0^∘ to 360^∘ range.

(θ_pos)=−135^∘+360^∘

(θ_pos)=225^∘

3. Identify the quadrant based on the standard ranges: Quadrant I (0^∘ to 90^∘, Quadrant II (90^∘ to 180^∘, Quadrant III (180^∘ to 270^∘, and Quadrant IV (270^∘ to 360^∘.

180^∘<225^∘<270^∘

Final Answer

Quadrant of −(3*π)/4=Quadrant III

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