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Math Help - Find the (trigonometric) limit

  1. #1
    s3a
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    Find the (trigonometric) limit

    How do I find the following limit?:

    lim t --> 0 (tan 6t)/(sin 2t)

    (The answer is 3 and I could also figure that out by plugging in t = 0.01 but I would like to know the legitimate way of doing this. My teacher taught us similar stuff but I don't think he went over this particular type of problem)

    Any help would be greatly appreciated!
    Thanks in advance!
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by s3a View Post
    How do I find the following limit?:

    lim t --> 0 (tan 6t)/(sin 2t)

    (The answer is 3 and I could also figure that out by plugging in t = 0.01 but I would like to know the legitimate way of doing this. My teacher taught us similar stuff but I don't think he went over this particular type of problem)

    Any help would be greatly appreciated!
    Thanks in advance!
    \lim_{t\rightarrow 0} \frac{\tan (6t)}{\sin (2t)}=\lim_{t\rightarrow 0} \frac{\tan (6t)}{6}\frac{2}{\sin(2t)}\frac{6}{2}=1*1*3=3
    Last edited by alexmahone; October 14th 2009 at 09:01 PM.
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  3. #3
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    note tan(6t)= sin(6t)/cos(6t).
    lim t->0 of cos6t=cos0=1
    multiply by (2t*3)/6t, then split the limits to
    sin(6t)/6t and sin(2t)/2t. you're left with two limits going to 1, a cos0=1 and and 3, so the limit is 3.
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