Find the Domain y=tan(x)+2

Problem

y=tan(x)+2

Solution

1. Identify the components of the function. The function y=tan(x)+2 consists of the trigonometric function tan(x) and a constant. The constant +2 does not restrict the domain.

2. Recall the definition of the tangent function. Since tan(x)=sin(x)/cos(x) the function is undefined whenever the denominator is zero.

3. Set the denominator equal to zero to find the excluded values. We must solve cos(x)=0

4. Solve for x The cosine function is zero at odd multiples of π/2 This is expressed as x=π/2+n*π where n is any integer.

5. State the domain. The domain consists of all real numbers except for these excluded values.

Final Answer

Domain={[x∈ℝ,x≠π/2+n*π,n∈ℤ]}

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