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Math Help - Converting Polar to Rectangular Equations

  1. #1
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    Exclamation Converting Polar to Rectangular Equations

    Was curious if anyone new how to find an equivalant equation in cartesian coordinates for the problem r=2sin@+2cos@ I have to turn in my trigonometry final tomorrow and am having problems with this one. I also am not sure how to make a theta so @ is theta. thank you...
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Thalstead View Post
    Was curious if anyone new how to find an equivalant equation in cartesian coordinates for the problem r=2sin@+2cos@ I have to turn in my trigonometry final tomorrow and am having problems with this one. I also am not sure how to make a theta so @ is theta. thank you...
    recall that r^2 = x^2 + y^2, also recall that, x = r \cos \theta and y = r \sin \theta

    so, start with r = 2 \sin \theta + 2 \cos \theta

    multiply through by r,

    \Rightarrow r^2 = 2r \sin \theta + 2r \cos \theta

    Now what?
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    Quote Originally Posted by Jhevon View Post
    recall that r^2 = x^2 + y^2, also recall that, x = r \cos \theta and y = r \sin \theta

    so, start with r = 2 \sin \theta + 2 \cos \theta

    multiply through by r,

    \Rightarrow r^2 = 2r \sin \theta + 2r \cos \theta

    Now what?


    The only next step that I can think would be to then have r^2=2y + 2x and possibly change the r^2 to x^2 + y^2
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Thalstead View Post
    The only next step that I can think would be to then have r^2=2y + 2x and possibly change the r^2 to x^2 + y^2
    yes. we want to get rid of the r's and the theta's and get x's and y's, so that's exactly what we do. so we get x^2 + y^2 = 2x + 2y. but what kind of curve is that?
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    I'm not really sure.... I was looking through the chapters in the book and didn't find anything similar. It wouldn't be a polar graph because we replaced the r's and theta's
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Thalstead View Post
    I'm not really sure.... I was looking through the chapters in the book and didn't find anything similar. It wouldn't be a polar graph because we replaced the r's and theta's
    of course it's not a polar graph anymore. it is a circle. now that you know that, could you say, find it's center and radius?
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    Smile

    Oh I understand now! yes I know how to work with circles! thank you so much for you're help. I really appreciate it =)
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