Evaluate cos(240 degrees )

Problem

cos(240^∘)

Solution

1. Identify the quadrant of the angle. Since 180^∘<240^∘<270^∘ the angle 240^∘ lies in Quadrant III.

2. Determine the sign of the cosine function. In Quadrant III, the cosine of an angle is negative.

3. Calculate the reference angle. The reference angle θ^′ for an angle in Quadrant III is found using θ^′=θ−180^∘

θ^′=240^∘−180^∘=60^∘

4. Apply the reference angle property. The value of cos(240^∘) is equal to −cos(60^∘)

5. Substitute the known value for cos(60^∘)

cos(60^∘)=1/2

cos(240^∘)=−1/2

Final Answer

cos(240^∘)=−1/2

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