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anonymous

  • one year ago

In the function f(x) = sec 2x, what are the following: - Domain - Asymptotes

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  1. SolomonZelman
    • one year ago
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    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.

  2. anonymous
    • one year ago
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    Wait, so \[\sec^2x \] is also \[\sec2x\]?

  3. anonymous
    • one year ago
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    Can I use the T-table to graph the function or nah?

  4. SolomonZelman
    • one year ago
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    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|

  5. anonymous
    • one year ago
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    Also, is there any way to find the domain without graphing?

  6. SolomonZelman
    • one year ago
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    wait, I thought you didn't use a caret (^), but your function is sec(2x)?

  7. anonymous
    • one year ago
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    Yup it is sec(2x).

  8. SolomonZelman
    • one year ago
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    So, it will be same as sec²x still. JUST THAT: the arcs will be thinner. the asymptote is everywhere when cos(x)=0

  9. SolomonZelman
    • one year ago
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    But it is still same, because if cos(x)=0, then cos²(x)=0 as well./

  10. anonymous
    • one year ago
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    Yes, that's why the range is \[(-\infty, -1], [1,\infty)\] correct?

  11. SolomonZelman
    • one year ago
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    yes

  12. SolomonZelman
    • one year ago
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    ((With a U in the middle ))

  13. SolomonZelman
    • one year ago
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    (-∞,-1] U [1,∞)

  14. anonymous
    • one year ago
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    oh yeah right. I thought you said no haha.

  15. anonymous
    • one year ago
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    So the period is pi.

  16. anonymous
    • one year ago
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    And there is no amplitude, right?

  17. SolomonZelman
    • one year ago
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    yes, period is π

  18. SolomonZelman
    • one year ago
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    yes no amplitude.

  19. SolomonZelman
    • one year ago
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    (I am lagging, my connection is bad)

  20. anonymous
    • one year ago
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    So the domain is all real nos. except ±π/4, ±3π/4, ±5π/4

  21. SolomonZelman
    • one year ago
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    yes\(\color{red}{,}\) no amplitude. (like that)

  22. SolomonZelman
    • one year ago
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    yes, and so on.... for all values tof x, that make cos(x)=0

  23. SolomonZelman
    • one year ago
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    of* x

  24. anonymous
    • one year ago
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    Also, in the book, it says the domain is all real nos except \[\frac{ \pi }{ 2}+\pi n\]

  25. anonymous
    • one year ago
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    What does it mean? Is it the same with what I stated above?

  26. SolomonZelman
    • one year ago
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    for all integer values of n.... that is the pattern in which these numbers are generated

  27. SolomonZelman
    • one year ago
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    i need to refresh. sorry. hold on.

  28. anonymous
    • one year ago
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    Okay, so how do I put the domain like that?

  29. SolomonZelman
    • one year ago
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    well, you can say that same thing in the book, and don't forget to add that \({n \in {\bf Z}\)

  30. SolomonZelman
    • one year ago
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    ops

  31. SolomonZelman
    • one year ago
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    So, you can state (for the asymptotes) that \(\large\color{black}{ \displaystyle \frac{\pi }{2} +\pi\cdot n;~\left\{n \in {\bf Z} \right\} }\)

  32. anonymous
    • one year ago
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    |dw:1437071434398:dw|

  33. SolomonZelman
    • one year ago
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    you can use wolframalpha.com to fill in the table.

  34. SolomonZelman
    • one year ago
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    it is a very cool calculator.

  35. anonymous
    • one year ago
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    No, I don't want just the answers.

  36. SolomonZelman
    • one year ago
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    What do you want then?

  37. anonymous
    • one year ago
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    I want to learn.

  38. SolomonZelman
    • one year ago
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    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.

  39. anonymous
    • one year ago
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    Yup, I want to plug the values myself.

  40. anonymous
    • one year ago
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    The thing is I don't know how to start. I just know that the "count number" is pi/4.

  41. anonymous
    • one year ago
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    \[\frac{ 1 }{ 4 } \times (period)\]

  42. SolomonZelman
    • one year ago
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    don't really know what 1/4 • period means

  43. anonymous
    • one year ago
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    Okay, so how would I find the x-values then?

  44. anonymous
    • one year ago
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    THANK YOU FOR THE HUGE HELP @SolomonZelman !

  45. anonymous
    • one year ago
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    oops didn't mean to use uppercase lol

  46. anonymous
    • one year ago
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    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...

  47. pooja195
    • one year ago
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    yes and?

  48. pooja195
    • one year ago
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    Can you pm and delete that reply please ?

  49. pooja195
    • one year ago
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    Im not a mod but i can talk to you about it.

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