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

Answer:

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

Step-by-step 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 $\pm \frac{\pi}{2}+n$.