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Math Help - General solution help

  1. #1
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    General solution help

    How do I answer questions like find all general solutions to :cos(x) = sin(x)?
    I know I need to get 2 different equations like x = 2npi +/- ... for cos and x = npi + (-1)^n ... but how do I get it so that cos(x) = ... and sin(x) = ... so I can apply the formula to the equation
    Last edited by guest12345; August 13th 2008 at 03:05 AM.
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hello,
    Quote Originally Posted by guest12345 View Post
    How do I answer questions like find all general solutions to :cos(x) = sin(x)?
    I know I need to get 2 different equations like x = 2npi +/- ... for cos and x = npi + (-1)^n ... but how do I get it so that cos(x) = ... and sin(x) = ... so I can apply the formula to the equation
    If \cos x=0, \sin x equals 1 or -1 so the equality \cos x=\sin x can't hold and \cos x must be different from 0. Thus we can safely divide both sides by \cos x and it gives us a new equation: 1=<br />
\frac{\sin x}{\cos x}\Longleftrightarrow 1=\tan x . Can you solve this ?
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  3. #3
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    yea but that's not what I was meaning, I was meaning if there's an equation with sin(4x) = cos(5x) (as posted in my new thread) or something of that nature then how do i solve it not for the equation in the post above, was just meaning that sort of equation in general, sorry if I was unclear.
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  4. #4
    Super Member flyingsquirrel's Avatar
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    Quote Originally Posted by guest12345 View Post
    yea but that's not what I was meaning, I was meaning if there's an equation with sin(4x) = cos(5x) (as posted in my new thread) or something of that nature then how do i solve it not for the equation in the post above, was just meaning that sort of equation in general, sorry if I was unclear.
    Then you can simply use \cos x = \sin \left(x+\frac{\pi}{2}\right)<br />
:

    <br />
\sin(4x)=\cos(5x) \Longleftrightarrow \sin(4x)=\sin\left(5x+\frac{\pi}{2} \right)\Longleftrightarrow  x\equiv\ldots
    Last edited by flyingsquirrel; August 14th 2008 at 12:13 AM.
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  5. #5
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    Quote Originally Posted by guest12345 View Post
    yea but that's not what I was meaning, I was meaning if there's an equation with sin(4x) = cos(5x) (as posted in my new thread) or something of that nature then how do i solve it not for the equation in the post above, was just meaning that sort of equation in general, sorry if I was unclear.
    This question has been answered as a consequence of solving the problem posted at http://www.mathhelpforum.com/math-he...-solution.html
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