Find the Exact Value cos(-150 degrees )

Problem

cos(−150)

Solution

1. Apply the even-odd identity for the cosine function, which states that cos(−θ)=cos(θ)

cos(−150)=cos(150)

2. Find the reference angle for 150 Since 150 is in the second quadrant, the reference angle is 180−150=30

(θ_ref)=30

3. Determine the sign of the cosine function in the second quadrant. Since cosine represents the x-coordinate on the unit circle, it is negative in the second quadrant.

cos(150)=−cos(30)

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

cos(150)=−√(,3)/2

Final Answer

cos(−150)=−√(,3)/2

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