Find the Exact Value cot(180)

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 θ=180 into the definition.

cot(180)=cos(180)/sin(180)

3. Determine the values of cos(180) and sin(180) using the unit circle.

cos(180)=−1

sin(180)=0

4. Evaluate the expression by substituting the values.

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

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