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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