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anonymous

  • 5 years ago

How does sin(t)/(1-cos(t)) simplify to cos(t)/sin(t)?

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  1. anonymous
    • 5 years ago
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    are you sure that's the exact question as written?

  2. anonymous
    • 5 years ago
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    It doesn't. Pick t=5 and you'll see it doesn't work.

  3. anonymous
    • 5 years ago
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    For example...

  4. anonymous
    • 5 years ago
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    Well it's that I'm looking at a solution my teacher wrote. He was showing how a cycloid had infinitely sharp cusps by finding the limit of the derivative of the parametric formulas given. So he was trying first to find the limit of sin(t)/(1-cos(t)) and he jumped to trying to find the limit of cos(t)/sin(t) because apparently, they're equal.

  5. anonymous
    • 5 years ago
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    Look at #5. http://people.sfcollege.edu/bruce.teague/pdf/2312%20W11/2312_MG5_solutions_W11.pdf This link should work.

  6. anonymous
    • 5 years ago
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    Did everybody leave?

  7. anonymous
    • 5 years ago
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    Awww c'mon!

  8. anonymous
    • 5 years ago
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    Now what am I gonna do?

  9. anonymous
    • 5 years ago
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    Calm down...I'll have a look.

  10. anonymous
    • 5 years ago
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    Haha ok

  11. anonymous
    • 5 years ago
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    Oh, he's used L'Hopital's rule...do you know about that?

  12. anonymous
    • 5 years ago
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    Maybe. I might have forgotten.

  13. anonymous
    • 5 years ago
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    I was about say that

  14. anonymous
    • 5 years ago
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    When you have indeterminate forms for the limit (numerator and denominator each go to something like 0/0 or infinity/infinity), the limit of the original ratio is equal to the limit ratio of the derivatives of the numerator and denominator.

  15. anonymous
    • 5 years ago
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    Take the derivative of the numerator of sin(t) and you get cos(t), and the derivative of 1-cost(t) is sin(t).

  16. anonymous
    • 5 years ago
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    Oh! It's all coming back now.

  17. anonymous
    • 5 years ago
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    OK. That makes sense. Thank you soooooo much.

  18. anonymous
    • 5 years ago
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    Fan me then! :) I want to reach superstar!

  19. anonymous
    • 5 years ago
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    How does one fan someone else?

  20. anonymous
    • 5 years ago
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    \[\lim_{t \rightarrow 0} \frac{sin(t)}{1-\cos(t)}= \frac{0}{1-1}=\frac{0}{0}\] lokisan is right, this is an indeterminate and using L'hopital would give you

  21. anonymous
    • 5 years ago
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    there should be a link-type thing next to my name..."Become a fan"

  22. anonymous
    • 5 years ago
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    I'm not seeing it. I'm looking.

  23. anonymous
    • 5 years ago
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    It's in the thread window...little 'thumbs up' icon. There's one next to your own name too.

  24. anonymous
    • 5 years ago
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    There. I got it.

  25. anonymous
    • 5 years ago
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    Awesome...cheers!

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spraguer (Moderator)
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