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Solving Trigonometric Equations with multiple solutions

  1. Dec 1, 2012 #1
    1. The problem statement, all variables and given/known data
    Solve each equation for solutions on the interval 0 ≤ x ≤ 2∏.
    Code (Text):

    2 sin x = √3
     
    3. The attempt at a solution
    Okay so I was able to solve this one:

    • 2 sin x = √3
    • sin x = (√3) / 2

    So i got x = ∏/3 ; 2∏/3 ; 4∏/3 ; 5∏/3

    I substituted the x's into the original problem, and ∏/3 and 2∏/3 give +(√3). The other two give -(√3). Are the one's that give negative results also solutions? If so, is this only true for (±√x), or is the sign always a significant factor?
     
  2. jcsd
  3. Dec 1, 2012 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    No, if [itex]sin(x)= -\sqrt{3}/2[/itex] then [itex]2sin(x)= -\sqrt{3}[/itex] which is NOT the original equation. Those values of x do NOT satisfy the equation and are NOT solutions. In particular, [itex]\sqrt{a}[/itex] is NOT the same as either [itex]-\sqrt{a}[/itex] or [itex]\pm\sqrt{a}[/itex].
     
  4. Dec 1, 2012 #3
    Thank you for clarifying (:
     
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