anonymous
  • anonymous
How does sin(t)/(1-cos(t)) simplify to cos(t)/sin(t)?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
are you sure that's the exact question as written?
anonymous
  • anonymous
It doesn't. Pick t=5 and you'll see it doesn't work.
anonymous
  • anonymous
For example...

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anonymous
  • anonymous
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.
anonymous
  • anonymous
Look at #5. http://people.sfcollege.edu/bruce.teague/pdf/2312%20W11/2312_MG5_solutions_W11.pdf This link should work.
anonymous
  • anonymous
Did everybody leave?
anonymous
  • anonymous
Awww c'mon!
anonymous
  • anonymous
Now what am I gonna do?
anonymous
  • anonymous
Calm down...I'll have a look.
anonymous
  • anonymous
Haha ok
anonymous
  • anonymous
Oh, he's used L'Hopital's rule...do you know about that?
anonymous
  • anonymous
Maybe. I might have forgotten.
anonymous
  • anonymous
I was about say that
anonymous
  • anonymous
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.
anonymous
  • anonymous
Take the derivative of the numerator of sin(t) and you get cos(t), and the derivative of 1-cost(t) is sin(t).
anonymous
  • anonymous
Oh! It's all coming back now.
anonymous
  • anonymous
OK. That makes sense. Thank you soooooo much.
anonymous
  • anonymous
Fan me then! :) I want to reach superstar!
anonymous
  • anonymous
How does one fan someone else?
anonymous
  • anonymous
\[\lim_{t \rightarrow 0} \frac{sin(t)}{1-\cos(t)}= \frac{0}{1-1}=\frac{0}{0}\] lokisan is right, this is an indeterminate and using L'hopital would give you
anonymous
  • anonymous
there should be a link-type thing next to my name..."Become a fan"
anonymous
  • anonymous
I'm not seeing it. I'm looking.
anonymous
  • anonymous
It's in the thread window...little 'thumbs up' icon. There's one next to your own name too.
anonymous
  • anonymous
There. I got it.
anonymous
  • anonymous
Awesome...cheers!

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