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anonymous
 one year ago
In the function f(x) = sec 2x, what are the following:
 Domain
 Asymptotes
anonymous
 one year ago
In the function f(x) = sec 2x, what are the following:  Domain  Asymptotes

This Question is Closed

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0Domain 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
 one year ago
Best ResponseYou've already chosen the best response.0Wait, so \[\sec^2x \] is also \[\sec2x\]?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Can I use the Ttable to graph the function or nah?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0Also, 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
 one year ago
Best ResponseYou've already chosen the best response.0Also, is there any way to find the domain without graphing?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0wait, I thought you didn't use a caret (^), but your function is sec(2x)?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0So, it will be same as sec²x still. JUST THAT: the arcs will be thinner. the asymptote is everywhere when cos(x)=0

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0But it is still same, because if cos(x)=0, then cos²(x)=0 as well./

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes, that's why the range is \[(\infty, 1], [1,\infty)\] correct?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0((With a U in the middle ))

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh yeah right. I thought you said no haha.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So the period is pi.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And there is no amplitude, right?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0yes, period is π

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0yes no amplitude.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0(I am lagging, my connection is bad)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So the domain is all real nos. except ±π/4, ±3π/4, ±5π/4

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0yes\(\color{red}{,}\) no amplitude. (like that)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0yes, and so on.... for all values tof x, that make cos(x)=0

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Also, in the book, it says the domain is all real nos except \[\frac{ \pi }{ 2}+\pi n\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What does it mean? Is it the same with what I stated above?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0for all integer values of n.... that is the pattern in which these numbers are generated

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0i need to refresh. sorry. hold on.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, so how do I put the domain like that?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0well, you can say that same thing in the book, and don't forget to add that \({n \in {\bf Z}\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0So, you can state (for the asymptotes) that \(\large\color{black}{ \displaystyle \frac{\pi }{2} +\pi\cdot n;~\left\{n \in {\bf Z} \right\} }\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437071434398:dw

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0you can use wolframalpha.com to fill in the table.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0it is a very cool calculator.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0No, I don't want just the answers.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0What do you want then?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0Oh, 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
 one year ago
Best ResponseYou've already chosen the best response.0Yup, I want to plug the values myself.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The thing is I don't know how to start. I just know that the "count number" is pi/4.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ 1 }{ 4 } \times (period)\]

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0don't really know what 1/4 • period means

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay, so how would I find the xvalues then?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0THANK YOU FOR THE HUGE HELP @SolomonZelman !

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oops didn't mean to use uppercase lol

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Domain: 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
 one year ago
Best ResponseYou've already chosen the best response.1Can you pm and delete that reply please ?

pooja195
 one year ago
Best ResponseYou've already chosen the best response.1Im not a mod but i can talk to you about it.
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