Find the Exact Value cot(150 degrees )

Problem

cot(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 cotangent function in the second quadrant. In the second quadrant, x is negative and y is positive, so cot(θ)=x/y is negative.

3. Apply the trigonometric identity for cotangent using the reference angle.

cot(150^∘)=−cot(30^∘)

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

cot(150^∘)=−√(,3)

Final Answer

cot(150^∘)=−√(,3)

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