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)

Want more problems? Check here!