Find the Exact Value cos(150)

Problem

cos(150^∘)

Solution

1. Identify the reference angle by finding the distance from the angle to the nearest 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. Recall the exact value of the cosine for the reference angle. The value of cos(30^∘) is √(,3)/2

4. Combine the sign and the value to find the final result.

Final Answer

cos(150^∘)=−√(,3)/2

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