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Calculating the length of a tangent curve

  1. May 17, 2012 #1
    Considering f(x) = tan(x) * 5 / 8 ......

    how can I find the length of the curve, specifically, between (0, 0) and (1, 1) ?

    if anyone can help I would be happy.

  2. jcsd
  3. May 17, 2012 #2

    You can't: the point (1,1) is not on the function's graph.

  4. May 18, 2012 #3
    Actually, it is... that's what the 5/8 is for. It shrinks the tangent vertically just enough for the curve to cross (-1,-1), (1,1), and (0,0).

    I still don't know how to go about finding the length of the curve though.

  5. May 18, 2012 #4
    Are you implying tan(1)*5/8= 1?
  6. May 18, 2012 #5

    No, it really doesn't: [itex]\,\tan 1=1.55741\Longrightarrow \frac{5}{8}\tan 1 = 0.97338\neq 1\Longrightarrow (1,1)\,[/itex] is not on the graph of the function, and neither

    is the point [itex]\,(-1,-1)\,[/itex]

  7. May 20, 2012 #6
    Ok, sorry, you're right... Thought it crossed 1,1 but that was based on a graph of it only.

    Still, anyone know how generally to find the length of a tangent curve?

  8. May 20, 2012 #7
    Check out the wikipedia entry on arclength where there are many formulas. Also, any calculus text will have arclength formulas. The key to them all is the Pythagorean theorem

    ds = sqrt(dx^2+dy^2). Divide out dx and you get sqrt(1+(dy/dx)^2) dx
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