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Math Help - Solve equation tanx=3sinx

  1. #1
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    Solve equation tanx=3sinx

    Hi just worked through this question:

    Solve the equation:
    tan(x) = 3sin(x)

    for -180 < 0 < 180

    I get cos(x) = 1/3

    and x = +- 70.5

    The answer says it's also +- 180 which makes sense but i wondered how this second result can be found?

    Thanks
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by aceband View Post
    Hi just worked through this question:

    Solve the equation:
    tan(x) = 3sin(x)

    for -180 < 0 < 180

    I get cos(x) = 1/3

    and x = +- 70.5

    The answer says it's also +- 180 which makes sense but i wondered how this second result can be found?

    Thanks
    EDIT: Does your book also give x=0 as a solution?

    As you have written it you are right but the book's answer suggest your limits are actually -180 \leq x \leq 180. This means \pm 180^o are allowable

    You are cancelling out sin(x) in the second step which is potentially equal to 0. Instead, solve this equation via factorising.

    \frac{sin(x)}{cos(x)} = 3sin(x)

    \frac{sin(x)-3sin(x)cos(x)}{cos(x)}=0

    sin(x)(1-3cos(x))=0

    Either: sin(x)=0 (which is where -180,0,180 comes from)

    or cos(x)=\frac{1}{3} which you did


    It is also interesting to note that this equation has a vertical asymptote at x= \pm 90^o
    Last edited by e^(i*pi); December 13th 2009 at 08:58 AM. Reason: see post
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