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!

Rotating Vector

  1. Mar 5, 2007 #1
    1. The problem statement, all variables and given/known data
    A vector x in R^2 is rotate twice through an angle theta (it is rotated through theta and again through theta). Find two expressions for the matrix representing this rotation. Verify that these two expressions are equivalent


    2. Relevant equations
    rotation matrix R=[cos, -sin; sin, cos]


    3. The attempt at a solution

    I can only think of one expression:

    (R)(R)(x).

    Could (R^2)(x) be the other one? How would i prove that this is equivalent?
     
    Last edited: Mar 5, 2007
  2. jcsd
  3. Mar 5, 2007 #2
    How about just rotating once by 2theta?
     
  4. Mar 5, 2007 #3
    follow up question: a vector x in R^2 is rotated n times through an angle theta. Find two expressions for the matrix representing this rotation. what identity is implied.

    if what Ziox said is true then it should be [cos (theta)n, -sin(theta)n; sin (theta)n, cos(theta)n]

    but i dont see what identity this implies?
     
  5. Mar 6, 2007 #4

    cristo

    User Avatar
    Staff Emeritus
    Science Advisor

    You should probably find a second expression for the matrix first.
     
  6. Mar 6, 2007 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    First, what is
    [tex]\left(\begin{array}{cc}cos(\theta) & -sin(\theta)\\ sin(\theta) & cos(\theta)\end{array}\right)^2[/tex]?

    Second, can you use trig identities to write that in terms of [itex]cos(2\theta)[/itex] and [itex] sin(2\theta)[/itex]?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?