Find the Quadrant of the Angle -(7pi)/6

Problem

−(7*π)/6

Solution

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

θ=−(7*π)/6⋅180/π

θ=−7⋅30

θ=−210

2. Find a coterminal angle between 0 and 360 by adding 360 to the negative angle.

(θ_coterminal)=−210+360

(θ_coterminal)=150

3. Determine 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.

90<150<180

Final Answer

Quadrant of −(7*π)/6=Quadrant II

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