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Math Help - Polar Equation

  1. #1
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    Polar Equation

    Convert the polar equation r=2cosx to rectangular coordinates and sketch the graph
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  2. #2
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    Quote Originally Posted by tiga killa View Post
    Convert the polar equation r=2cosx to rectangular coordinates and sketch the graph
    r should be r=2\cos(\theta) since r is a function of the angle theta. The x and y coordinates can be found by the standard conversion:

    x=r\cos(\theta)
    y=r\sin(\theta)

    Look at this page for a nice explanation of common polar graphs. Yours should graph a circle.

    Pauls Online Notes : Calculus II - Polar Coordinates
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  3. #3
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by tiga killa View Post
    Convert the polar equation r=2cosx to rectangular coordinates and sketch the graph
    I assume you meant \theta instead of x?

    Multiply through by r to get r^2=2r\cos(\theta)

    We know that r^2=x^2+y^2 and that x=r\cos(\theta) so our new equation is:

    x^2+y^2=2x \implies x^2-2x+1-1+y^2=0 \implies \boxed{(x-1)^2+y^2=1}

    So it's a circle of radius 1 centered at (1,0).
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