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Cos and sin relations

  1. Aug 31, 2009 #1
    if

    [tex] \mu = cos(\theta) [/tex] and [tex] \mu_{0} = cos(\theta_{0}) [/tex]

    and

    [tex] cos(\pi - \Theta) = \mu_{0}\mu + \sqrt{1-\mu_{0}^{2}}\sqrt{1-\mu^{2}}cos(\phi) [/tex]

    Then

    [tex] cos(\pi - \Theta) = cos(\theta_{0})cos(\theta) + sin(\theta_{0})sin(\theta)cos(\phi) [/tex]


    Is this not correct?
     
  2. jcsd
  3. Aug 31, 2009 #2
    What if one of the sines is negative?
     
  4. Aug 31, 2009 #3
    sorry, range of [tex]\theta[/tex] is 0 to 60 degrees, and [tex] \theta_{0} [/tex] range is 0 to 70 degrees. As far as I can tell, sin will always be positive. But regardless, sin(theta)< 0 would change the value of the over all equation, but are the two equations not equal?
     
  5. Aug 31, 2009 #4
    Several questions:

    (1) Are [itex]\theta[/itex] and [itex]\Theta[/itex] the same variable?

    (2) What is [itex]\phi[/itex]?

    (3) I'm not sure what the equation is getting at. It appears to be a hyrid of a cofunction, symmetric, and angle sum identity. Something feels missing. Could you provide more detail as to what you are trying to show here?

    --Elucidus
     
  6. Aug 31, 2009 #5

    Integral

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    Yes, your final relationship follows from what you have given.
     
  7. Sep 1, 2009 #6
    Ok thanks Integral; I just wanted to make sure I wasn't crazy
     
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