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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