# Thread: Asymptote of equation with secant?

1. ## Asymptote of equation with secant?

Basically, I'm given the equation: y= 5csc(7x) and I'm being asked for one x= asymptote.

How would I go about solving this without a calculator?

edit: accidentally mistyped the title as secant. Should be cosecant.

2. $cosec(x)=\frac{1}{sin(x)}$ so it has asymptotes where $sin(x)=0$.

$sin(x)=0$ at $x=n\pi,\ \ n\in J$

Hence, for your question you can solve $7x=n\pi$ to find the asymptotes.

e.g. where $n=1$ there is an asymptote at $\frac{\pi}{7}$