Find the Asymptotes y=tan(x)

Problem

y=tan(x)

Solution

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

y=sin(x)/cos(x)

2. Determine the condition for vertical asymptotes by finding where the denominator of the function is equal to zero.

cos(x)=0

3. Solve for x to find the values where the cosine function vanishes.

x=π/2+n*π

4. Define the integer variable n to represent all possible vertical asymptotes across the domain.

n∈ℤ

5. Check for horizontal asymptotes by evaluating the limit of the function as x approaches infinity.

(lim_x→∞)(tan(x))=undefined

Final Answer

x=π/2+n*π,n∈ℤ

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