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Radian and Arcsine Help

  1. Jun 7, 2012 #1
    1. The problem statement, all variables and given/known data

    Find x in radians using [0,2pi]

    Sin(3x)= -0.1658

    2. Relevant equations

    -None-

    3. The attempt at a solution

    3x=Sin-1(-0.1658)

    x=sin-1(-0.1658)/3

    x= -0.055523061

    The teacher gave me a whole page to do the problem, so I don't know if there should be more work or not. Not positive if this answer is correct also.
     
  2. jcsd
  3. Jun 7, 2012 #2
    I believe that there should be 6 answers to this equation.
     
  4. Jun 7, 2012 #3
    Ok, could you help me get them? I don't understand this question at all.
     
  5. Jun 7, 2012 #4
    Your work was all right, and your answer is in fact a zero of the equation. But it doesn't lie in the domain you are looking for.

    When solving these equations, think of the unit circle.
    sin and the height of the circle are related. So solving for when the sin(x) = -.1658, can you see how many solutions are?
     
  6. Jun 7, 2012 #5
    Here are some hints:

    sin (pi - θ) = sinθ
    sin(2n*pi-θ)=-sinθ
    plus other similar relations

    chet
     
  7. Jun 7, 2012 #6
    I still don't understand. If I could get the answers, I could try back-tracking to get the work and understand how to do it.
     
  8. Jun 7, 2012 #7
    You need to think logically about your answer; it's not in the range 0 to 2pi. You have a negative angle that has this sine. What positive angles in the range 0 to 2pi will have that sine?
     
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