Evaluate cos(120 degrees )

Problem

cos(120^∘)

Solution

1. Identify the reference angle by finding the distance from the angle to the nearest xaxis.

(θ_ref)=180^∘−120^∘=60^∘

2. Determine the quadrant of the angle 120^∘

90^∘<120^∘<180^∘

Quadrant II

3. Determine the sign of the cosine function in Quadrant II.

cos(θ)<0

4. Apply the reference angle value for cos(60^∘)

cos(60^∘)=1/2

5. Combine the sign and the value to find the final result.

cos(120^∘)=−1/2

Final Answer

cos(120^∘)=−1/2

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