Calc

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Find a cartesian equation for the curve described by the given polar equation.
a. r=2
b. r=3sin pheta
c.r^2=sin2pheta

I don't understand how to solve for this, especially for r squared. Would someone plz explain how o convert to a cartesian equation. any help would be greatly appreciated!

  • Calc -

    The relationships you need should be in your text, or you can find them at the top of
    http://mathworld.wolfram.com/PolarCoordinates.html

    your first one r = 2 is then quite easy

    r = √(x^2 + y^2)

    2 = √(x^2 + y^2)
    x^2 + y^2 = 4 which is a circle

    your second:

    r=3sin pheta
    r=3sinß

    but sinß = y/r
    r=3sinß
    r = 3(y/r)
    r^2 = 3y
    x^2 + y^2 = 3y

    for the third I can't tell if you mean

    r^2 = sin(2ß) or r^2 = sin2ß

    I will let you decide and then follow my previous examples.

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