1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Parametric and Cartesian Equations

  1. Oct 29, 2006 #1
    ok I am give a parametric equations of

    x= 4 cos t and y=5 sin t

    I know that i have to solve the x equation for t then stick it in the y equation but i getting stuck or not rembering some simple stuff i should be.

    I believe i get t= cos(inv) (x/4) and substiute it in to t in y.

    if so how so i simplify

    5 sin(cos(inv)(x/4))
     
  2. jcsd
  3. Oct 29, 2006 #2
    [tex] \frac{x}{4} = \cos t [/tex]


    [tex] \frac{y}{5} = \sin t [/tex]


    [tex] \sin^{2} t + \cos^{2}t = 1 [/tex]
     
  4. Oct 29, 2006 #3
    so then i would justs substiute in those in so it would be
    x^2/16 +y^2/25
     
  5. Oct 29, 2006 #4

    Hootenanny

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Don't forget they equal one.
     
  6. Oct 29, 2006 #5

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    in general, sin(arcos(x)) can be solved by drawing a right triangle. arcos(x) is an angle theta whose cosine is x. So pick one of the angles that's not 90 degrees. Label that theta. Since theta is arcos(x), the adjacent side is x, and the hypotenuse is 1. So sin(theta) is opposite over hypotenuse. You can get the opposite side by pythagoras, and you're done.
     
  7. Oct 29, 2006 #6
    ok i understnad that now but how would you do the reverse.. go form given a cartesian equation to a cause given X^2-y^2=1 how would you solve that
     
  8. Oct 29, 2006 #7

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    You're trying to make that into a parametric form? We know cosh2t - sinh2t = 1. so if you let x=cosht, and y=sinht, it works

    In general, if you're completely at a loss, you can try to solve for y=f(x), let x=t, and y=f(t)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Parametric and Cartesian Equations
Loading...