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Simultaneous Trig Equations

  1. Sep 23, 2010 #1
    How would one go about solving the following equation?

    242= 290cos(theta) + 187cos(phi)
    0 = 290sin(theta) - 187sin(phi)

    I have tried squaring both sides of both equations and adding them, and then using cos2x + sin2x = 1 to narrow some stuff down, and basically only found that:

    phi + theta = 123.9 degrees.

    But I still feel like I'm stuck. Maybe I'm missing an identity or something, I am terrible with those. Any help would be appreciated.
  2. jcsd
  3. Sep 23, 2010 #2
    Just realized I put this in the wrong forum,....sorry guys.
  4. Sep 24, 2010 #3
    Since this is homework, here are some strategy hints

    Call your equations above 1,2,3

    From 1 get cos[tex]\phi[/tex] in terms of cos[tex]\theta[/tex]

    From 2 get sin[tex]\phi[/tex] in terms of sin[tex]\theta[/tex]

    substitute into either the formula for

    cos ([tex]\theta[/tex] + [tex]\phi[/tex])


    sin ([tex]\theta[/tex] + [tex]\phi[/tex])

    Substituting into 3 will get you an equation in a single unknown.
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