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

Want more problems? Check here!