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Math Help - Writing expression in terms of t=tan x/2

  1. #1
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    Writing expression in terms of t=tan x/2

    Stuck on this one question.

    3cosx + 4sinx, write in terms of t=tan x/2

    The answer is 3 - 3t^2 +8t / 1+t^2

    Sorry I just wrote it in normal text, in a hurry lol.

    Thanks
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  2. #2
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    Hello icesta1
    Quote Originally Posted by icesta1 View Post
    Stuck on this one question.

    3cosx + 4sinx, write in terms of t=tan x/2

    The answer is 3 - 3t^2 +8t / 1+t^2

    Sorry I just wrote it in normal text, in a hurry lol.

    Thanks
    Provided you know the formulae:
    \sin x = \frac{2t}{1+t^2} and \cos x = \frac{1-t^2}{1+t^2}
    I don't see what the problem is. Just substitute these into the expression, and the answer follows immediately:
    3\cos x +4\sin x = \frac{3(1-t^2)}{1+t^2}+ \frac{8t}{1+t^2}
    =\frac{3-3t^2+8t}{1+t^2}
    Have you seen these formulae before?

    Grandad
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  3. #3
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    Hm... its funny cause I actually have that written in my book lol. I think i might have been looking at the wrong answer while doing it >_< lol.

    Thanks anyways

    EDIT: Nvm i got it
    Last edited by icesta1; March 3rd 2010 at 11:43 PM.
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