# Confusion of finding asymtotes from trig function

• Feb 1st 2011, 06:25 PM
johnsy123
Confusion of finding asymtotes from trig function
I am having a hard time on comprehending where the asymptotes lie on a variety of trig questions.

y= sec(x/2) > [0,2pie]
-the help sheet clearly states that when plotting a sec graph, the asymptotes are located in the domain of [0,2pie] at pie/2 and 3pie/2, but the answer repels this and has the asymptotes at just pie. What am i doing wrong?

y= cot(3x) > [0,2pie]
-the help sheet clear states that the asymptotes are located in the domain of [0,2pie] at 0,pie and 2 pie, yet the answer locates the asymptotes at pie/3, 2pie/3, pie, 4pie/3, 5pie/3 and 2pie........why are there more than the normal amount? is it because there is a number in the brackets, making there more cycles therefor more asymptotes, i am unsure. It would be very helpful if someone could provide me with a bit of detail on this.
• Feb 1st 2011, 06:27 PM
dwsmith
Quote:

Originally Posted by johnsy123
I am having a hard time on comprehending where the asymptotes lie on a variety of trig questions.

y= sec(x/2) > [0,2pie]
-the help sheet clearly states that when plotting a sec graph, the asymptotes are located in the domain of [0,2pie] at pie/2 and 3pie/2, but the answer repels this and has the asymptotes at just pie. What am i doing wrong?

y= cot(3x) > [0,2pie]
-the help sheet clear states that the asymptotes are located in the domain of [0,2pie] at 0,pie and 2 pie, yet the answer locates the asymptotes at pie/3, 2pie/3, pie, 4pie/3, 5pie/3 and 2pie........why are there more than the normal amount? is it because there is a number in the brackets, making there more cycles therefor more asymptotes, i am unsure. It would be very helpful if someone could provide me with a bit of detail on this.

Note that

$\dispalystyle \sec(x)=\frac{1}{\cos(x)} \ \ \ \cot(x)=\frac{1}{\tan(x)}$

Whenever cosine is 0, the sec graph will have an asymptote, and the same applies to tangent.

The question you should ask yourself is where is $\cos\left(\frac{x}{2}\right)= 0$ in the defined interval and like wise for tangent.
• Feb 1st 2011, 06:41 PM
skeeter
Quote:

Originally Posted by johnsy123
I am having a hard time on comprehending where the asymptotes lie on a variety of trig questions.

y= sec(x/2) > [0,2pie]
...

this is pi ...

http://ualr.edu/lasmoller/mathresources/bigpi.gif

... and this is pie.

http://scienceblogs.com/corpuscallos...umpkin_pie.jpg