Find the Value Using the Unit Circle cos(150 degrees )

Problem

cos(150^∘)

Solution

1. Identify the position of 150^∘ on the unit circle. Since 90^∘<150^∘<180^∘ the angle terminates in the second quadrant.

2. Determine the reference angle by subtracting the angle from 180^∘

(θ_ref)=180^∘−150^∘=30^∘

3. Recall the cosine value for the reference angle 30^∘ from the unit circle.

cos(30^∘)=√(,3)/2

4. Apply the sign based on the quadrant. In the second quadrant, the xcoordinate (cosine) is negative.

cos(150^∘)=−cos(30^∘)

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

cos(150^∘)=−√(,3)/2

Final Answer

cos(150^∘)=−√(,3)/2

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