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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