Evaluate cos(150 degrees )

Problem

cos(150^∘)

Solution

1. Identify the reference angle by finding the distance from the angle to the nearest x-axis (180^∘.

(θ_ref)=180^∘−150^∘=30^∘

2. Determine the quadrant of the angle 150^∘ which lies in Quadrant II.

3. Determine the sign of the cosine function in Quadrant II, where cosine values are negative.

cos(150^∘)=−cos(30^∘)

4. Substitute the known exact value for cos(30^∘) which is √(,3)/2

cos(150^∘)=−√(,3)/2

Final Answer

cos(150^∘)=−√(,3)/2

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