Simplify 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. Substitute the value 0 into the trigonometric identity.

cot(0)=cos(0)/sin(0)

3. Evaluate the numerator and denominator using the unit circle values for 0 radians.

cos(0)=1

sin(0)=0

4. Determine the result of the division by zero.

cot(0)=1/0

5. Conclude that since division by zero is not defined in the real number system, the expression is undefined.

Final Answer

cot(0)=undefined

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