Find the Domain tgx

Problem

tan(x)

Solution

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

tan(x)=sin(x)/cos(x)

2. Determine the condition for the domain by identifying where the expression is undefined. The function is undefined when the denominator is zero.

cos(x)=0

3. Solve for the values of x where the cosine function equals zero. This occurs at odd multiples of π/2

x=π/2+n*π

n∈ℤ

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

x≠π/2+n*π

Final Answer

Domain of *tan(x)={[x∈ℝ,x≠π/2+n*π,n∈ℤ]}

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