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Solving an equation involving sin and cos terms

  1. Mar 3, 2009 #1
    Hi

    I was wondering if there is a non-numericla way to solve the following equation:

    144 - 90sin x - 155.8cos x = 0

    Thanks
     
  2. jcsd
  3. Mar 3, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    That's not a nice equation but here's what I might do: write it as 90 sin x= 144- 155.8 cos x
    [itex]90\sqrt{1- cos^2 x}= 144- 155.8 cos x[/itex] and square both sides to get [itex]8100(1- cos^2 x)= 20736- 44870.4cos x+ 24273.64cos^2 x[/itex]. Solve that quadratic equation for cos x and then take the arccosine to find x. When you square both sides of an equation, that new equation may have roots that do not satisfy the original equation.
     
  4. Mar 3, 2009 #3
    Thank you!
     
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