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I Angle at which cardioid hits the x-axis

  1. Dec 4, 2016 #1
    How can we find the angle at wich the curve of equation : r=b + acosθ hits the x-axis.
    I want a fast way or method since I only need it to plot the graph well. I'm only asked to plot the curve well and pay attention to the angle at which the curve hits the x-axis and not to calculate and write how I got it.
     
  2. jcsd
  3. Dec 4, 2016 #2

    BvU

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    Looks like homework to me ... needs your attempt at solution. You know, PF rules and all that.

    By the way, acosθ is slightly ambiguous...

    upload_2016-12-4_13-21-40.png
     
    Last edited: Dec 4, 2016
  4. Dec 4, 2016 #3

    BvU

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    Fair enough.
    upload_2016-12-4_13-23-56.png
    So what you want is ##\displaystyle {dy\over dx}## at y = 0, right ?
    Write ##\ y = y(r,\theta) = y(\theta)\ ## and ##\ x = x(r,\theta) = x(\theta)\ ##
    Take derivatives
    Divide
    On the way you see you need derivatives at ##\theta = 0, \ \theta = \pi## that are trivial.
    The other two or four (at ##x=0## ) require some work.
    I know of no quicker way.
    (except using excel to cheat drawing the pictures :wink:)
    upload_2016-12-4_13-34-21.png
     
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