Find the Value Using the Unit Circle cot(0)

Problem

cot(0)

Solution

1. Identify the definition of the cotangent function in terms of sine and cosine.

cot(θ)=cos(θ)/sin(θ)

2. Determine the coordinates on the unit circle for the angle 0 radians.

(x,y)=(cos(0),sin(0))

3. Evaluate the cosine and sine values at 0 using the unit circle.

cos(0)=1

sin(0)=0

4. Substitute these values into the cotangent formula.

cot(0)=1/0

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

Final Answer

cot(0)=undefined

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