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Math Help - addition formula,

  1. #1
    Junior Member
    Joined
    Jan 2009
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    57

    addition formula,

    Hi,

    I have a proof for cos( \theta + \delta) = cos \theta cos\delta - sin \theta sin \delta

    Apparently by writing (\frac{\pi}{2}-\delta) for \delta and using cos(\frac{\pi}{2}-\delta)=sin \delta and vice versa

    I get
    sin(\theta + \delta)=sin \theta cos \delta + cos \theta sin \delta. I cannot get this result, not with the signs correct.

    cos(\theta + [\frac{\pi}{2}-\delta])=cos \theta sin \delta - sin \theta cos \delta
    cos(\frac{\pi}{2}-[\delta - \theta])=...
    we get
    sin(\delta - \theta)=sin \delta cos \theta - cos \delta sin \theta

    I am supposed to get
    sin(\theta + \delta)=sin \theta cos \delta + cos \theta sin \delta

    I am doing something wrong with the signs or something.
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  2. #2
    MHF Contributor
    Joined
    Nov 2008
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    France
    Posts
    1,458
    Quote Originally Posted by craigmain View Post
    Hi,

    I have a proof for cos( \theta + \delta) = cos \theta cos\delta - sin \theta sin \delta

    Apparently by writing (\frac{\pi}{2}-\delta) for \delta and using cos(\frac{\pi}{2}-\delta)=sin \delta and vice versa

    I get
    sin(\theta + \delta)=sin \theta cos \delta + cos \theta sin \delta. I cannot get this result, not with the signs correct.

    cos(\theta + [\frac{\pi}{2}-\delta])=cos \theta sin \delta - sin \theta cos \delta

    cos(\frac{\pi}{2}-[\delta - \theta])=...
    we get
    sin(\delta - \theta)=sin \delta cos \theta - cos \delta sin \theta

    I am supposed to get
    sin(\theta + \delta)=sin \theta cos \delta + cos \theta sin \delta

    I am doing something wrong with the signs or something.
    Hi

    If your starting point is \cos( \theta + \delta) = \cos \theta \cos\delta - \sin \theta \sin \delta

    and you want to find \sin(\theta + \delta)=\sin \theta \cos \delta + \cos \theta \sin \delta

    you can do like this

    \sin(\theta + \delta) = \cos\left(\frac{\pi}{2}-(\theta + \delta)\right)

    \sin(\theta + \delta) = \cos\left(\left(\frac{\pi}{2}-\theta\right) + (-\delta)\right)

    \sin(\theta + \delta) = \cos \left(\frac{\pi}{2}-\theta\right) cos(-\delta) - \sin \left(\frac{\pi}{2}-\theta\right) \sin (-\delta)

    \sin(\theta + \delta) = \sin \theta cos \delta + \cos \theta \sin \delta
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  3. #3
    Junior Member
    Joined
    Jan 2009
    Posts
    57
    Thanks, I was trying to do it on the wrong side. Silly.
    There's an art to stating the obvious that will take a lifetime to learn.
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