Find the Exact Value cot(pi)

Problem

cot(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 π into the trigonometric definitions.

cot(π)=cos(π)/sin(π)

3. Evaluate the cosine and sine values at π radians using the unit circle.

cos(π)=−1

sin(π)=0

4. Determine the result of the division by zero.

cot(π)=(−1)/0

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

Final Answer

cot(π)=undefined

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