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Solutions to trig Equation

  1. Oct 22, 2012 #1
    Hi,

    I have the answers to the following question, but i do not know how to calculate them from the first:

    Find all the solutions to the following equation

    Sin( (5x)/2 + 15°) = 0.34

    Where 0°≤x≥360°

    The answers are (1.950749625,58.04925038,145.9507496,202.0492504,289.9507496,346.0492504)

    My attempt

    sin-1(0.34)=19.88

    19.88-15 = 4.88

    (4.88*2)/5 = 1.95

    How are the other answer worked out from here?

    Thanks
     
  2. jcsd
  3. Oct 22, 2012 #2

    SammyS

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    The general solution to [itex]\displaystyle \ \sin(\theta)=u\ [/itex] is [itex]\displaystyle \ \theta=\sin^{-1}(u)+(360^\circ) k\,,\ 180^\circ-\sin^{-1}(u)+(360^\circ) k\,, [/itex] where k is an integer.
     
  4. Oct 22, 2012 #3

    HallsofIvy

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    Do you know what the graph of y= sin(x) looks like? It is positive for [itex]0\le x\le 180[/itex] and negative for [itex]180\le x\le 360[/itex]. And, between 0 and 180, the graph is symmetric: [itex]sin(180- x)= sin(x)[/itex].
     
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