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Trig Asymptotes

  1. Aug 30, 2014 #1
    1. The problem statement, all variables and given/known data

    Find the equation of the asymptotes.
    On the interval -pi < x < pi

    2. Relevant equations

    tan(2 sin x)

    3. The attempt at a solution

    sin(2 sin x)/cos( 2 sin x)

    Set cos( 2 sin x) = 0

    2 sin x = arccos(0) = pi/2
    2 sin x = arccos(0) = -pi/2

    x = +-(arcsin pi/4)

    But these are only but two asymptotes on the interval -pi < x < pi of tan( 2 sin x)-- yet when graphed; there are 4 observed.
     
  2. jcsd
  3. Aug 30, 2014 #2

    Simon Bridge

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    Use what you know of the tangent function directly.
    tan has assymtotes when it's argument is a particular series of numbers - what are they?
    2sin(x) can only evaluate to two of those numbers - what are they?
    How many times does 2sin(x) visit each of those numbers in the interval?
     
  4. Aug 30, 2014 #3
    Haha whilst formulating my response... I saw the light! Thank you so much!!!

    Great way to start the day, and good one to ya!
     
  5. Aug 30, 2014 #4

    Simon Bridge

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    Often the way - well done.
     
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