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Math Help - polar to rect form conversion

  1. #1
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    polar to rect form conversion

    Hi. I'm working on a practice problem which is stumping me. Even after looking up the answer in the back of the book, I still don't understand how it was arrived at.

    The question involves taking polar equation

    r = 2(h*cos(t)+k*sin(t))

    And coverting it to rectangular form, and verifying that it is the equation of a circle.

    I keep playing around with the coord conversion equations and trig identities, but I can't seem to get it worked out. Help!
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  2. #2
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    Re: polar to rect form conversion

    Quote Originally Posted by infraRed View Post
    Hi. I'm working on a practice problem which is stumping me. Even after looking up the answer in the back of the book, I still don't understand how it was arrived at.

    The question involves taking polar equation

    r = 2(h*cos(t)+k*sin(t))

    And coverting it to rectangular form, and verifying that it is the equation of a circle.

    I keep playing around with the coord conversion equations and trig identities, but I can't seem to get it worked out. Help!
    r = \sqrt{x^2 + y^2}, cos(t) = \frac{x}{\sqrt{x^2 + y^2}}, and sin(t) = \frac{y}{\sqrt{x^2 + y^2}}

    Hint: Plug these into your equation and multiply both sides by \sqrt{x^2 + y^2}.

    -Dan
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    Re: polar to rect form conversion

    Quote Originally Posted by infraRed View Post
    Hi. I'm working on a practice problem which is stumping me. Even after looking up the answer in the back of the book, I still don't understand how it was arrived at.

    The question involves taking polar equation

    r = 2(h*cos(t)+k*sin(t))

    And coverting it to rectangular form, and verifying that it is the equation of a circle.

    I keep playing around with the coord conversion equations and trig identities, but I can't seem to get it worked out. Help!
    if (h \neq k) then it's not a circle, it's an ellipse.
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