Find the Exact Value cot(2pi)

Problem

cot(2*π)

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 θ=2*π into the expression.

cot(2*π)=cos(2*π)/sin(2*π)

3. Evaluate the trigonometric values for the angle 2*π on the unit circle.

cos(2*π)=1

sin(2*π)=0

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

cot(2*π)=1/0

5. Conclude that since division by zero is undefined, the cotangent of 2*π does not exist.

Final Answer

cot(2*π)=Undefined

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