Find the Exact Value cos(120)

Problem

cos(120^∘)

Solution

1. Identify the reference angle by finding the distance from the angle to the x-axis. Since 120^∘ is in the second quadrant, the reference angle is 180^∘−120^∘=60^∘

2. Determine the sign of the cosine function in the second quadrant. In the second quadrant, the x-coordinates are negative, so cos(120^∘) must be negative.

3. Apply the reference angle property.

cos(120^∘)=−cos(60^∘)

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

cos(120^∘)=−1/2

Final Answer

cos(120^∘)=−1/2

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