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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