Find the Domain y=cot(x)

Problem

y=cot(x)

Solution

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

cot(x)=cos(x)/sin(x)

2. Determine the condition for the domain by identifying where the function is undefined. A fraction is undefined when the denominator is equal to zero.

sin(x)=0

3. Solve the equation for x to find the excluded values. The sine function is zero at all integer multiples of π

x=n*π

n∈ℤ

4. State the domain as all real numbers except for the values where the function is undefined.

{[x∈ℝ,x≠n*π,n∈ℤ]}

Final Answer

Domain of *cot(x)={[x∈ℝ,x≠n*π,n∈ℤ]}

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