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Homework Help: Solving Equations Using the Unit Circle

  1. May 11, 2010 #1
    1. The problem statement, all variables and given/known data

    Find all solutions to the equation below such that -180° [tex]\leq[/tex] x [tex]\leq[/tex] 90°

    2sin2x + sinx = 0


    2. Relevant equations



    3. The attempt at a solution

    2sin2x + sinx = 0

    sinx[2sinx + 1] = 0

    sin x = 0 sinx= -1/2

    x = {0° + 360°n
    {-180° + 360°n
    n[tex]\epsilon[/tex]I
     
    Last edited: May 11, 2010
  2. jcsd
  3. May 11, 2010 #2

    Mark44

    Staff: Mentor

    x = n*pi are the solutions to sin(x) = 0. What about the solutions to sin(x) = -1/2?
     
  4. May 11, 2010 #3
    im not using equations, i am getting my exact values from the unit circle
     
  5. May 11, 2010 #4
    Yeah, Mark44! :rofl:
     
  6. May 11, 2010 #5

    Mark44

    Staff: Mentor

    You are using equations, namely 2sin2x + sinx = 0, which you rewrote as sinx(2sinx + 1) = 0.

    You have found the solutions to the equation sinx = 0, but you haven't found any for the equation 2sinx + 1 = 0.

    BTW, according to your problem description, you need be concerned only with values for which -180° <= x <= 90°. On this interval there are only two solutions to sinx = 0.
     
  7. May 11, 2010 #6
    If you post an equation here, it looks like you're using it.
    sin x = 1/2 is another possibility. I'm certain that value of x is on the unit circle as well.
    you didn't use the condition that -180<=x<=90. An answer such as 360n isn't acceptable here.
     
  8. May 11, 2010 #7

    Mark44

    Staff: Mentor

    Probably a typo, but sin x = 1/2 is not a solution. sin x = -1/2 is a solution, though.
     
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