Simplify cot(150)

Problem

cot(150)

Solution

1. Identify the reference angle for 150 by subtracting it from 180 because it is in the second quadrant.

180−150=30

2. Determine the sign of the cotangent function in the second quadrant.

In Quadrant II, *cot(θ)<0

3. Apply the reference angle identity for cotangent.

cot(150)=−cot(30)

4. Evaluate the cotangent of the reference angle using the ratio of cosine to sine.

cot(30)=cos(30)/sin(30)

5. Substitute the known values for cos(30) and sin(30)

cot(30)=√(,3)/2/1/2

6. Simplify the fraction.

cot(30)=√(,3)

7. Combine the value with the negative sign determined in step 2.

cot(150)=−√(,3)

Final Answer

cot(150)=−√(,3)

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