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!

Rotate a linear function

  1. Jun 26, 2013 #1
    1. The problem statement, all variables and given/known data
    I have two coordinate system [itex](x, y)[/itex], [itex](x', y')[/itex] that differ by a rotation around the [itex]z[/itex]-axis by an angle [itex]\alpha[/itex]. In the coordinate system [itex](x', y')[/itex] I have a function [itex]f(x', y') = C[/itex], where [itex]C[/itex] is a constant.

    I would like to express [itex]f[/itex] in the coordinate system [itex](x,y)[/itex], where it is a linear function [itex]x\nabla +y_0[/itex]. The gradient [itex]\nabla[/itex] of this function is [itex]1/\tan(\alpha)[/itex].


    3. The attempt at a solution
    I need to find the shift in [itex]x[/itex] now. I get that this is [itex]C/\cos(\alpha)[/itex]. Is there a way for me to test that this function indeed is constant in the coordinate system [itex](x', y')[/itex]?
     
  2. jcsd
  3. Jun 26, 2013 #2

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Draw a picture of f(x',y') = C in your x'-y' coordinate system. Now imagine that this coordinate system is rotated about the origin by an angle alpha. What happens to the line f(x',y') = C? Don't you need more than one parameter to express this line in the (x,y) system?
     
  4. Jun 26, 2013 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Rotation about the z-axis through an angle [itex]\alpha[/itex] is given by the matrix
    [tex]\begin{bmatrix}cos(\alpha) & -sin(\alpha) & 0 \\ sin(\alpha) & cos(\alpha) & 0 \\ 0 & 0 & 1\end{bmatrix}[/tex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Rotate a linear function
  1. Rotating a function (Replies: 1)

  2. Linear Functions (Replies: 3)

Loading...