Find the Exact Value cot(-150 degrees )

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. Find the reference angle for 150^∘ Since 150^∘ is in the second quadrant, the reference angle is 180^∘−150^∘=30^∘

Reference Angle=30^∘

3. Determine the sign of the cotangent function in the second quadrant. In the second quadrant, cotangent is negative.

cot(150^∘)=−cot(30^∘)

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

cot(150^∘)=−√(,3)

5. Apply the negative sign from the first step to find the final value.

−cot(150^∘)=−(−√(,3))

cot(−150^∘)=√(,3)

Final Answer

cot(−150^∘)=√(,3)

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