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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