Find the Exact Value cot(-150)

Problem

cot(−150)

Solution

1. Use the odd-even property of the cotangent function, which states that cot(−θ)=−cot(θ)

cot(−150)=−cot(150)

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

Reference Angle=30

3. Identify the sign of the cotangent function in the second quadrant. In Quadrant II, cotangent is negative.

cot(150)=−cot(30)

4. Substitute this back into the expression from step 1.

−cot(150)=−(−cot(30))

cot(−150)=cot(30)

5. Evaluate the cotangent of the reference angle using the known value cot(30)=√(,3)

cot(30)=√(,3)

Final Answer

cot(−150)=√(,3)

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