Find the Value Using the Unit Circle cos(210)

Problem

cos(210^∘)

Solution

1. Identify the position of the angle 210^∘ on the unit circle. Since 180^∘<210^∘<270^∘ the angle lies in the third quadrant.

2. Calculate the reference angle by subtracting 180^∘ from the given angle.

(θ_ref)=210^∘−180^∘=30^∘

3. Determine the sign of the cosine function in the third quadrant. In the third quadrant, the xcoordinates are negative, so cos(210^∘) must be negative.

4. Apply the reference angle value from the unit circle. The cosine of 30^∘ is √(,3)/2

cos(210^∘)=−cos(30^∘)

5. Substitute the known value to find the final result.

cos(210^∘)=−√(,3)/2

Final Answer

cos(210^∘)=−√(,3)/2

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