Results 1 to 4 of 4

Math Help - Converting from Polar form to Rectangular form

  1. #1
    Newbie
    Joined
    Apr 2009
    From
    Washington state
    Posts
    12

    Arrow Converting from Polar form to Rectangular form

    If you have the time,

    So i want to convert this polar equation to a rectangular form.
    Problem1: r= 4cosθ - 4sinθ


    I understand the simple conversions like this one:
    r= 3secθ
    r/secθ = 3 (divided secθ)
    rcosθ = 3 (1/secθ = cosθ)
    x = 3 : rcosθ = x (coordinate conversion equations)

    but i dont know how to begin with the problem 1

    Here are other coordinate conversion equations that might help:
    y = rsinθ
    r^2 = x^2 + y^2
    tanθ = y/x

    thankyou!
    Last edited by yeunju; April 26th 2009 at 10:18 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by yeunju View Post
    If you have the time,

    So i want to convert this polar equation to a rectangular form.
    Problem1: r= 4cosθ - 4sinθ
    Hint: multiply through by r, you get

    r^2 = 4r \cos \theta - 4 r \sin \theta

    now what?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2009
    From
    Washington state
    Posts
    12
    Oh, with that helpful hint
    i'm thinking to use the x=rcosθ and y=rsinθ and r^2 = x^2+y^2
    so: x^2 + y^2 = 4x - 4y
    then maybe x^2 -4x + y^2 + 4y = 0

    I remember an example with my teacher using complete the square? but it was on an equation like x^2 + y^2 = 4x (subtract 4x)
    so then it ended up with x^2 -4x +4 +y^2 = 4

    so could i do that with both x and y? maybe..
    or am i going the wrong direction?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member redsoxfan325's Avatar
    Joined
    Feb 2009
    From
    Swampscott, MA
    Posts
    943
    Yes, rewrite it as x^2 -4x +4 +y^2 +4y+4 = 8.

    Complete the square for both x and y to get:

    Spoiler:
    (x-2)^2+(y+2)^2=8

    Voila! It's a circle of radius 2\sqrt{2} centered at (2,-2).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: August 17th 2009, 11:43 PM
  2. Rectangular form into Polar Form
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: May 30th 2009, 11:04 AM
  3. converting rectangular equations into polar form
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: May 25th 2009, 11:16 PM
  4. converting polar equations into rectangular form
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: May 25th 2009, 09:40 PM
  5. From polar form to rectangular form..help!
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: June 6th 2006, 10:26 PM

Search Tags


/mathhelpforum @mathhelpforum