Find the Exact Value cot(-180 degrees )

Problem

cot(−180)

Solution

1. Identify the definition of the cotangent function in terms of sine and cosine.

cot(θ)=cos(θ)/sin(θ)

2. Substitute the given angle into the definition.

cot(−180)=cos(−180)/sin(−180)

3. Evaluate the cosine and sine values at −180 using the unit circle.

cos(−180)=−1

sin(−180)=0

4. Determine the existence of the value by checking the denominator.

cot(−180)=(−1)/0

5. Conclude that since division by zero is undefined, the cotangent of −180 does not exist.

Final Answer

cot(−180)=undefined

Want more problems? Check here!