Results 1 to 6 of 6

Math Help - Given one set of coordinates, find another set that is 120 degrees away.

  1. #1
    Newbie
    Joined
    Apr 2012
    From
    United States
    Posts
    2

    Given one set of coordinates, find another set that is 120 degrees away.

    given the set of coordinates (-1035,-410) how would i go about finding another set of coordinates that is 120 degrees away?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,792
    Thanks
    1687
    Awards
    1

    Re: Given one set of coordinates, find another set that is 120 degrees away.

    Quote Originally Posted by justinjrichards View Post
    given the set of coordinates (-1035,-410) how would i go about finding another set of coordinates that is 120 degrees away?
    What does "120 degrees away" mean to you?
    Please explain.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2012
    From
    United States
    Posts
    2

    Re: Given one set of coordinates, find another set that is 120 degrees away.

    its been a while since i took trig. so my terminology may be incorrect, but if the given coordinates are on the circumference of the circle then there could be two more sets of coordinates on the circle that are 120 degrees apart. one set clockwise 120 degrees and another set counter clockwise 120 degrees. the center of the circle would be at (0,0) i believe.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,792
    Thanks
    1687
    Awards
    1

    Re: Given one set of coordinates, find another set that is 120 degrees away.

    Quote Originally Posted by justinjrichards View Post
    its been a while since i took trig. so my terminology may be incorrect, but if the given coordinates are on the circumference of the circle then there could be two more sets of coordinates on the circle that are 120 degrees apart. one set clockwise 120 degrees and another set counter clockwise 120 degrees. the center of the circle would be at (0,0) i believe.
    If (-1035,-410) is on a circle centered at (0,0) then the radius is 1113.25.
    You posted this in a trigonometry forum. The answer I will give may not look correct in trig terms.

    This is done with a rotation matrix, a transformation.
    \left( {x\cos (\theta ) - y\sin (\theta ),x\sin (\theta ) + y\cos (\theta )} \right) is the resulting point of rotating the point (x,y) about (0,0) through an angle of \theta.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,872
    Thanks
    656

    Re: Given one set of coordinates, find another set that is 120 degrees away.

    Quote Originally Posted by justinjrichards View Post
    given the set of coordinates (-1035,-410) how would i go about finding another set of coordinates that is 120 degrees away?
    let (x_1,y_1) be the starting set of coordinates.

    r = \sqrt{x_1^2 + y_1^2}

    since x_1 and y_1 are both negative, the angle of the ray that passes thru (x_1,y_1) is \theta = \arctan\left(\frac{y_1}{x_1}\right) + 180^\circ

    120^\circ "away" could be (\theta + 120^\circ) or (\theta - 120^\circ)

    new coordinates could be (r\cos(\theta + 120^\circ),r\sin(\theta + 120^\circ)) or (r\cos(\theta - 120^\circ),r\sin(\theta - 120^\circ))
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,792
    Thanks
    1687
    Awards
    1

    Re: Given one set of coordinates, find another set that is 120 degrees away.

    With regard to reply #5 there is a way to simply cut to the chase directly.
    Using \left( {x\cos (\theta ) - y\sin (\theta ),x\sin (\theta ) + y\cos (\theta )} \right) let x=-1035~\&~y=-410 then take two cases \theta =\pm 120^o.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. How to find the value of sin45 degrees?
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: April 3rd 2011, 09:13 AM
  2. [SOLVED] Find the exact value of tan -105 degrees
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: February 28th 2011, 08:14 PM
  3. Find the degrees.
    Posted in the Geometry Forum
    Replies: 4
    Last Post: February 17th 2010, 05:41 AM
  4. Replies: 6
    Last Post: December 21st 2009, 05:54 PM
  5. Replies: 2
    Last Post: April 6th 2009, 09:19 AM

Search Tags


/mathhelpforum @mathhelpforum