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Find the length of curve r=cos(theta)-sin(theta)

  1. May 6, 2014 #1
    1. The problem statement, all variables and given/known data

    Find the length of the curve r=cosΘ - sinΘ, 0≤Θ≤∏/4

    2. Relevant equations

    Arc length = ∫|v| dt

    3. The attempt at a solution

    I found r'(θ), then used the arc length formula.

    Arc length = ∫ sqrt (sin^2 Θ + cos^2 Θ) = ∫ dΘ

    and integrated it to find ∫dΘ = ∏/4

    The correct answer is however ∏/(2sqrt(2)). Where did I go wrong?
     
    Last edited: May 6, 2014
  2. jcsd
  3. May 6, 2014 #2

    SteamKing

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    We can't guess unless you post your work.
     
  4. May 6, 2014 #3

    LCKurtz

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    I will guess that he is confusing a parametric (vector) equation of a curve with a polar coordinate equation of a curve.
     
  5. May 6, 2014 #4
    Could you possibly expand on this? I am not sure what you mean.
     
  6. May 6, 2014 #5

    Curious3141

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    There is quite a different formula for the length of a curve in polar coordinates. It is ##\displaystyle s = \int_{\theta_1}^{\theta_2}\sqrt{r^2 + {(\frac{dr}{d\theta})}^2}d\theta.## When you apply some trig identities, the problem becomes very simple.
     
  7. May 6, 2014 #6

    LCKurtz

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    Your given equation is not a parametric equation like ##\vec r(t)=\langle x(t),y(t)\rangle## so your arc length formula doesn't apply. It is a polar coordinate equation like ##r = f(\theta)##. Look up the formula for arc length for a polar coordinate equation.
     
  8. May 6, 2014 #7
    Thanks so much. I didn't realize there was another formula.
     
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