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Math Help - polar representation

  1. #1
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    polar representation

    Hi theres this problem : give the polar representation for the circle of radius 3 centered at (0,3).

    I got the equation of the circle : x^2+(y-3)^2=9
    Also I know how to change a single point into polar coords. Basicly just draw a triangle and do trig. but how do you turn a equation into polar? Im stumped.
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  2. #2
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    x = r\cdot\cos(\theta)
    y = r\cdot\sin(\theta)

    Seriously, that's it.
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  3. #3
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    Quote Originally Posted by frankinaround View Post
    Hi theres this problem : give the polar representation for the circle of radius 3 centered at (0,3).

    I got the equation of the circle : x^2+(y-3)^2=9
    Also I know how to change a single point into polar coords. Basicly just draw a triangle and do trig. but how do you turn a equation into polar? Im stumped.
    or you can do it like this

    x = r\cdot\cos(\theta)
    y-3 = r\cdot\sin(\theta)
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  4. #4
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    well I get that y should be 3Sin(theta) and x should be 3cos(theta). I guess that any point that that works out for will be on the circle for either. but where is the origin in this equation ? Also the answer is supposed to be R=6sin(theta) so im like huh?
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  5. #5
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    Quote Originally Posted by frankinaround View Post
    well I get that y should be 3Sin(theta) and x should be 3cos(theta). I guess that any point that that works out for will be on the circle for either. but where is the origin in this equation ? Also the answer is supposed to be R=6sin(theta) so im like huh?
    Given an arbitrary point (x, y) extend a line from the origin to the point (x, y). Call the length of this line r and the angle it makes with the +x axis (theta). Using basic trigonometry you can find that x = r*cos(theta) and y = r*sin(theta). Note that the angle (theta) must be measured from the +x axis and not the -x axis.

    @ sedam7 y-3 = r*sin(theta) can be used but you must bear in mind that your equation gives a vertical translation of the original y axis. The substitution y = r*sin(theta) is more appropriate here.

    As to the rest:







    Now simplify. Note that
    .

    -Dan
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