Find the Exact Value cos(210 degrees )

Problem

cos(210^∘)

Solution

1. Identify the quadrant of the angle. Since 180^∘<210^∘<270^∘ the angle 210^∘ 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^′=210^∘−180^∘=30^∘

4. Apply the reference angle property. The value of cos(210^∘) is equal to −cos(30^∘)

5. Substitute the known exact value for cos(30^∘) which is √(,3)/2

cos(210^∘)=−√(,3)/2

Final Answer

cos(210^∘)=−√(,3)/2

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