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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