Simplify cos(120)

Problem

cos(120)

Solution

1. Identify the angle in the coordinate plane. The angle 120 is in the second quadrant.

2. Determine the reference angle. For an angle θ in the second quadrant, the reference angle is 180−θ

180−120=60

3. Apply the cosine sign rule for the second quadrant. In the second quadrant, the cosine function is negative.

cos(120)=−cos(60)

4. Substitute the known value for the cosine of the reference angle. The value of cos(60) is 1/2

cos(120)=−1/2

Final Answer

cos(120)=−1/2

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