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Homework Help: Finding the tangent and normal of a trigonometric equation?

  1. Sep 29, 2011 #1
    1. The problem statement, all variables and given/known data
    a. find the tangent and normal line at P (0,0)
    b. find when the tangent is horizontal

    Equation: 3x+sin3x at (0,0)

    3. The attempt at a solution
    Find the derivative- y'=3 (?) or it it 3x+cos(3x)?
    But from there, I don't know how to find the rate of change to create a new equation. I usually find the slope, get the x and y point values (for this problem, the points are given) and use y-y1=m(x-x1).
  2. jcsd
  3. Sep 29, 2011 #2


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    Neither. Of course it has two terms but you need the chain rule for the second term.

    You just need the slope at (0,0) so put in x = 0 once you have the correct derivative and you will have your m.
  4. Sep 29, 2011 #3
    I'm not sure I follow. Is sin3x a product of sin and 3x?
    I thought sin3x was a single term.
  5. Sep 29, 2011 #4


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    It is sin(3x). The derivative of sin(x) is cos(x). But you don't have sin(x). Look in your calculus book about the chain rule.
  6. Sep 29, 2011 #5
    chain rule:
    if you have

    take the derivative of the inside "g(x)", and multiply it by the derivative of the outside "f(x)":

    So say we have a similar problem:

    2x[itex]^{2}[/itex]+ x + cos(5x)

    The derivative would be

    4x + 1 - 5sin(5x)

    Plugging in zero would give you
    1 - 5sin(0)


    so the answer for this example would be 1
    now try the same method on your problem
    Last edited: Sep 29, 2011
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