Question

Where does the graph of the function y=tan(x) have asymptotes?

Answer 1

At every pi/2 that doesn't result in a whole number value of pi. so 3pi/2, 5pi/2, etc..

Answer 2

`y=\text{tan}(x)` will have asymptote, when
`\text{cos}(x)=0`.

Explanation:

We are asked to find the asymptotes of the function
`y=\text{tan}(x)`.

We can represent tangent as
`\text{tan}(x)=\frac{\text{sin}(x)}{\text{cos}(x)}`.

We know that a rational function is undefined, when denominator is zero. So our function will have asymptote, when
`\text{cos}(x)=0`.

We know that
`\text{cos}(x)=0` at
`\pm (\pi)/(2)+n`.