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Tangent Line and Coordinates of Trigonometric Function

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

    There are infinitely many points on the curve y = [tex]\frac{sin x}{\sqrt{2}- cos x}[/tex] at which the tangent line to this curve is horizontal. Find the x- and y-coordinates of one such point.

    2. Relevant equations

    y' = slope of the tangent line
    Etc., etc.

    3. The attempt at a solution
    I know you have to take the derivative of the given equation, and at first, I tried using the quotient rule, but I got nowhere with that. Then I tried rationalizing the [tex]\sqrt{2}[/tex], but that didn't really get me anywhere either. I also have no idea how to find the x- and y-coordinates.

    All help is greatly appreciated!
  2. jcsd
  3. May 1, 2010 #2
    Nothing needs to be done with [tex]\sqrt{2}[/tex], it is a constant. What's the derivative of a constant? (btw, [tex]\sqrt{2}[/tex] is an irrational number which is why you couldn't rationalize it.)

    The coordinates are the x and y-values of the function and y=f(x) so, (x,y)=(x,f(x))
  4. May 1, 2010 #3
    To the OP, please show us your work in taking the derivative using the quotient rule. I did the same and got a particularly pleasing answer.
  5. May 2, 2010 #4
    I got something like [tex]\frac{1-cos^2(x)}{2-cos^2(x)}[/tex].
    I'm not sure if this right at all. My prowess with the quotient rule is shoddy at best.
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