Results 1 to 3 of 3

Math Help - Confusing polar coordinates

  1. #1
    Member
    Joined
    Jan 2010
    Posts
    104

    Confusing polar coordinates

    Find Cartesian coordinates for all points of intersection of the curves given below:
    r=1-sin(theta) and r^2=4sin(theta)
    Sketch these.

    I am not sure how to do this. Do you square the r=1-sin(theta) and set it equal to 4 sin (theta) and solve for theta? That seems complicated. What is the best approach?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Dec 2009
    From
    1111
    Posts
    872
    Thanks
    3
    Quote Originally Posted by twittytwitter View Post
    Find Cartesian coordinates for all points of intersection of the curves given below:
    r=1-sin(theta) and r^2=4sin(theta)
    Sketch these.

    I am not sure how to do this. Do you square the r=1-sin(theta) and set it equal to 4 sin (theta) and solve for theta? That seems complicated. What is the best approach?
    Dear twittytwitter,

    (1-sin\theta)^2=r^2=4sin\theta

    1-6sin\theta+sin^{2}\theta=0

    (sin\theta-3)^{2}-9+1=0

    (sin\theta-3)^{2}=8

    sin\theta-3=\pm{\sqrt{8}}

    sin\theta=3\pm{2\sqrt{2}}

    Since, sin\theta\leq{1}\Rightarrow{sin\theta=3-2\sqrt{2}}

    sin\theta=3-2\sqrt{2}

    This value satisfies both the given equations.

    Therefore, \theta=n\pi+(-1)^{n}sin^{-1}(3-2\sqrt{2}) ; where n\in{Z}

    Hope this helps.
    Last edited by Sudharaka; March 10th 2010 at 07:06 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jan 2010
    Posts
    104
    thank you
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 10
    Last Post: September 24th 2010, 04:33 AM
  2. Polar coordinates
    Posted in the Geometry Forum
    Replies: 1
    Last Post: March 29th 2009, 04:48 PM
  3. Replies: 6
    Last Post: February 4th 2009, 12:12 AM
  4. Polar Coordinates and Polar Graphs
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: October 2nd 2007, 04:44 PM
  5. polar coordinates
    Posted in the Calculus Forum
    Replies: 4
    Last Post: February 15th 2007, 12:39 PM

Search Tags


/mathhelpforum @mathhelpforum