How to find the asymptotes of $y = \frac{1}{2} sec (x - \frac{π}{6})$ $y = 1/2 sec ( x - pi/6)$ ?

Question

2631 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-08-12T09:27:01

$x=2kpi+(3pi)/2 and x=2kpi-pi/3 , kinZZ$

$y=1/2sec(x-pi/6)=1/2*1/cos(x-pi/6)$

We know that when $cos(x-pi/6)rarr0$ then $yrarrpmoo$
so everytime that $cos(x-pi/6)=0$ the function has a vertical asymptode.

Let's solve the equation $cos(x-pi/6)=0$ :

$cos(x-pi/6)=0iffcos(x-pi/6)=cos(pi/2)iff$

$x-pi/6=2kpipmpi/2iff x=2kpi+(2pi)/3or x=2kpi-pi/3$

So the function has the folowing vertical asyptodes :

$x=2kpi+(3pi)/2 and x=2kpi-pi/3 , kinZZ$

How to find the asymptotes of y = 1/2 sec ( x - pi/6)y=12sec(x−π6)y = 1/2 sec ( x - pi/6)?