Find the Quadrant of the Angle 120

Problem

120^∘

Solution

1. Identify the standard position of the angle. An angle in standard position has its vertex at the origin and its initial side along the positive xaxis.

2. Recall the degree ranges for each quadrant in a coordinate plane:

• Quadrant I: 0^∘<θ<90^∘

• Quadrant II: 90^∘<θ<180^∘

• Quadrant III: 180^∘<θ<270^∘

• Quadrant IV: 270^∘<θ<360^∘

3. Compare the given angle 120^∘ to these ranges.

4. Determine that since 90^∘<120^∘<180^∘ the terminal side of the angle lies in the second quadrant.

Final Answer

Quadrant of *120^∘=Quadrant II

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