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Convert y=3x+4 to Polar form

  1. Sep 12, 2007 #1
    1. The problem statement, all variables and given/known data
    Write equation in polar form. y=3x+4

    2. Relevant equations
    x^2 + y^2 = r^2
    x = rcos(theta)
    y = rsin(theta)
    tan(theta) = y/x

    3. The attempt at a solution

    Square both sides...
    y^2 = 9x^2 + 24x + 16

    r^2 - x^2 = 9x^2 +24x +16

    r^2 = 10x^2 + 24x + 16

    And that's where I got stuck...
  2. jcsd
  3. Sep 12, 2007 #2


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    Homework Helper

    Don't do it like that. Substitute the polar form of x and y into your equation... and you'll be done.
  4. Sep 12, 2007 #3


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    Staff Emeritus
    Science Advisor

    Replace EVERY x with [itex]r cos(\thet[/itex] and EVERY y with [itex]r sin(\theta)[/itex]
  5. Sep 12, 2007 #4
    What is your goal in converting from Cartesian to polar coordinates? You want to get a function that is:
    r = a bunch of theta junk

    So how do we turn y=3x+4 into an equation of nothing but r’s and theta’s? We use the two substations you have, then we get r all by it self on one side.
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