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Math Help - reducing trig functions to a single function

  1. #1
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    reducing trig functions to a single function

    Hi
    I'm trying to reduce a function in the form
    Acos(x)+Bsin(x)
    to a single function.
    I know that to do this you need to multiply and divide by sqrt(A^2+B^2), but I don't know where to go from there. Can anyone help with this?
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  2. #2
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    Quote Originally Posted by Defiant View Post
    Hi
    I'm trying to reduce a function in the form
    Acos(x)+Bsin(x)
    to a single function.
    I know that to do this you need to multiply and divide by sqrt(A^2+B^2), but I don't know where to go from there. Can anyone help with this?
    \sqrt{A^2 + B^2} \left(\frac{A}{\sqrt{A^2 + B^2}} \cos x + \frac{B}{\sqrt{A^2 + B^2}} \sin x \right)

    Now define \tan \phi = \frac{A}{B} and use the compound angle formula. You get \sqrt{A^2 + B^2} \sin (x + \phi).
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  3. #3
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    Thanks alot...kinda stupid, that was the only thing my entire DE was stuck on...
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