Find the Exact Value cos(-120 degrees )

Problem

cos(−120)

Solution

1. Apply the even-odd identity for the cosine function, which states cos(−θ)=cos(θ)

cos(−120)=cos(120)

2. Find the reference angle for 120 by subtracting it from 180 because it is in the second quadrant.

Reference Angle=180−120=60

3. Determine the sign of the cosine function in the second quadrant. Since cosine is negative in the second quadrant, the value will be negative.

cos(120)=−cos(60)

4. Substitute the known value for cos(60) which is 1/2

−cos(60)=−1/2

Final Answer

cos(−120)=−1/2

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