Find the Exact Value cos(150 degrees )

Problem

cos(150)

Solution

1. Identify the reference angle by finding the distance from the terminal side to the x-axis. Since 150 is in the second quadrant, the reference angle is 180−150=30

2. Determine the sign of the cosine function in the second quadrant. In the second quadrant, the x-coordinates are negative, so cos(150) must be negative.

3. Apply the reference angle rule which states that cos(θ)=±cos((θ_ref)) In this case, cos(150)=−cos(30)

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

Final Answer

cos(150)=−√(,3)/2

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