Find the Value Using the Unit Circle cos(120)

Problem

cos(120^∘)

Solution

1. Identify the position of the angle 120^∘ on the unit circle. Since 90^∘<120^∘<180^∘ the angle lies in Quadrant II.

2. Determine the reference angle by subtracting the angle from 180^∘

(θ_ref)=180^∘−120^∘=60^∘

3. Recall the cosine value for the reference angle 60^∘ from the unit circle.

cos(60^∘)=1/2

4. Apply the appropriate sign for the cosine function in Quadrant II. In Quadrant II, xcoordinates (cosine values) are negative.

cos(120^∘)=−cos(60^∘)

5. Substitute the known value to find the final result.

cos(120^∘)=−1/2

Final Answer

cos(120^∘)=−1/2

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