Find the Exact Value cos(210)

Problem

cos(210)

Solution

1. Identify the quadrant of the angle. Since 180<210<270 the angle 210 lies in the third quadrant.

2. Determine the reference angle. In the third quadrant, the reference angle (θ_ref) is calculated as θ−180

(θ_ref)=210−180=30

3. Apply the sign for the cosine function. In the third quadrant, the cosine of an angle is negative.

cos(210)=−cos(30)

4. Substitute the known exact value for cos(30)

cos(30)=√(,3)/2

5. Combine the sign and the value to find the final result.

cos(210)=−√(,3)/2

Final Answer

cos(210)=−√(,3)/2

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