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Homework Help: Sin(arctan(x/4))= ?

  1. Aug 25, 2014 #1
    [Mentor's note: This thread was originally posted in a non-homework forum, so it doesn't follow the homework template.]


    Sin(arctan(x/4))= ?

    Been over 2 years since Ive done some math, a little help please?
    Last edited by a moderator: Aug 25, 2014
  2. jcsd
  3. Aug 25, 2014 #2


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    Set up a right triangle with sides x and 4, so that the tangent of one of the angles is x/4, i.e., tanθ=x/4. Then θ=tan^{-1}(x/4) . From the drawing, figure out the value of sinθ.
  4. Aug 25, 2014 #3


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    It might help you if you draw a triangle and split the expression above into component parts.

    First, how would you triangle look if you were to show what arctan(x/4) meant?
  5. Aug 25, 2014 #4
    Ok I:

    Drew a triangle in quadrant 1 to represent x/4 and labeled the angle A for random sake
    then used Pythagorean theorem to find the hyp
    after solving for sign and rationalizing I came up with:

    SinA= (x(√(x^2)+16)/((x^2)+16) ------ √ ending after the first 16
    sound right?
  6. Aug 25, 2014 #5


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    Yes, ##\sin(A)=x\frac{\sqrt{x^2+16}}{x^2+16}##.

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