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 of 180^∘ into the trigonometric functions.

cot(180^∘)=cos(180^∘)/sin(180^∘)

3. Determine the coordinates of the point on the unit circle at 180^∘ which are (−1,0)

cos(180^∘)=−1

sin(180^∘)=0

4. Evaluate the expression by substituting the values of cosine and sine.

cot(180^∘)=(−1)/0

5. Conclude that since the denominator is zero, the value is undefined.

Final Answer

cot(180^∘)=undefined

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