Find the Quadrant of the Angle -240

Problem

−240^∘

Solution

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

−240^∘+360^∘=120^∘

2. Identify the quadrant boundaries for standard position angles.

Quadrant I:0^∘<θ<90^∘

Quadrant II:90^∘<θ<180^∘

Quadrant III:180^∘<θ<270^∘

Quadrant IV:270^∘<θ<360^∘

3. Compare the angle to the boundaries. Since 120^∘ is between 90^∘ and 180^∘ the angle lies in the second quadrant.

90^∘<120^∘<180^∘

Final Answer

−240^∘⇒Quadrant II

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