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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