anonymous
  • anonymous
In the function f(x) = sec 2x, what are the following: - Domain - Asymptotes
Mathematics
chestercat
  • chestercat
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SolomonZelman
  • SolomonZelman
Domain will have gaps. \(f(x)=\sec^2(x)\) \(f(x)=\displaystyle \frac{1}{ \cos^2(x)}\) so for every value where cos²(x)=0, you have a vertical asymptote.
anonymous
  • anonymous
Wait, so \[\sec^2x \] is also \[\sec2x\]?
anonymous
  • anonymous
Can I use the T-table to graph the function or nah?

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SolomonZelman
  • SolomonZelman
Also, you know that |cos x| < |sec x| And cos(x) (as well as sine), is between 1 and -1. This way, |sec x| is always ≥1 and ≤-1. So, it will look roughly like this: |dw:1437070613045:dw|
anonymous
  • anonymous
Also, is there any way to find the domain without graphing?
SolomonZelman
  • SolomonZelman
wait, I thought you didn't use a caret (^), but your function is sec(2x)?
anonymous
  • anonymous
Yup it is sec(2x).
SolomonZelman
  • SolomonZelman
So, it will be same as sec²x still. JUST THAT: the arcs will be thinner. the asymptote is everywhere when cos(x)=0
SolomonZelman
  • SolomonZelman
But it is still same, because if cos(x)=0, then cos²(x)=0 as well./
anonymous
  • anonymous
Yes, that's why the range is \[(-\infty, -1], [1,\infty)\] correct?
SolomonZelman
  • SolomonZelman
yes
SolomonZelman
  • SolomonZelman
((With a U in the middle ))
SolomonZelman
  • SolomonZelman
(-∞,-1] U [1,∞)
anonymous
  • anonymous
oh yeah right. I thought you said no haha.
anonymous
  • anonymous
So the period is pi.
anonymous
  • anonymous
And there is no amplitude, right?
SolomonZelman
  • SolomonZelman
yes, period is π
SolomonZelman
  • SolomonZelman
yes no amplitude.
SolomonZelman
  • SolomonZelman
(I am lagging, my connection is bad)
anonymous
  • anonymous
So the domain is all real nos. except ±π/4, ±3π/4, ±5π/4
SolomonZelman
  • SolomonZelman
yes\(\color{red}{,}\) no amplitude. (like that)
SolomonZelman
  • SolomonZelman
yes, and so on.... for all values tof x, that make cos(x)=0
SolomonZelman
  • SolomonZelman
of* x
anonymous
  • anonymous
Also, in the book, it says the domain is all real nos except \[\frac{ \pi }{ 2}+\pi n\]
anonymous
  • anonymous
What does it mean? Is it the same with what I stated above?
SolomonZelman
  • SolomonZelman
for all integer values of n.... that is the pattern in which these numbers are generated
SolomonZelman
  • SolomonZelman
i need to refresh. sorry. hold on.
anonymous
  • anonymous
Okay, so how do I put the domain like that?
SolomonZelman
  • SolomonZelman
well, you can say that same thing in the book, and don't forget to add that \({n \in {\bf Z}\)
SolomonZelman
  • SolomonZelman
ops
SolomonZelman
  • SolomonZelman
So, you can state (for the asymptotes) that \(\large\color{black}{ \displaystyle \frac{\pi }{2} +\pi\cdot n;~\left\{n \in {\bf Z} \right\} }\)
anonymous
  • anonymous
|dw:1437071434398:dw|
SolomonZelman
  • SolomonZelman
you can use wolframalpha.com to fill in the table.
SolomonZelman
  • SolomonZelman
it is a very cool calculator.
anonymous
  • anonymous
No, I don't want just the answers.
SolomonZelman
  • SolomonZelman
What do you want then?
anonymous
  • anonymous
I want to learn.
SolomonZelman
  • SolomonZelman
Oh, I mean not a graphing calc. I mean to find particular values of cse(2x), if you want. Or, you can plug the values yourself, and calculate them yourself. And if you encounter a problem calculating (by hand) one value or the other, you can ask me.
anonymous
  • anonymous
Yup, I want to plug the values myself.
anonymous
  • anonymous
The thing is I don't know how to start. I just know that the "count number" is pi/4.
anonymous
  • anonymous
\[\frac{ 1 }{ 4 } \times (period)\]
SolomonZelman
  • SolomonZelman
don't really know what 1/4 • period means
anonymous
  • anonymous
Okay, so how would I find the x-values then?
anonymous
  • anonymous
THANK YOU FOR THE HUGE HELP @SolomonZelman !
anonymous
  • anonymous
oops didn't mean to use uppercase lol
anonymous
  • anonymous
Domain: all real numbers other than: ±π/4, ±3π/4, ±5π/4... Range:(-∞,-1) U (1,∞) Period: π Asymptotes:x=±π/4, x=±3π/4, x=±5π/4...
pooja195
  • pooja195
yes and?
pooja195
  • pooja195
Can you pm and delete that reply please ?
pooja195
  • pooja195
Im not a mod but i can talk to you about it.

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