# Linear algebra rotation

1. Jan 27, 2013

hi,
I understand how to do the rotation equation

A = [ cosθ -sinθ
sinθ cosθ]

A*v = [ cosθ -sinθ * [ x = [ xcosθ - ysinθ
sinθ cosθ] y ] xsinθ + ycosθ ]

A*v = [ cos90 -sin90 * [ 6
sin90 cos90 ] 4 ]

= [ 0, -1 * [ 6 = [ 0 * 6 - 1 * 4 = [ -4
1, 0 ] 4 ] 1 * 6 + 0 * 4 ] 6 ]

but the text book I am using doesn't go into using different angle as you can see this is a 90 degree equation but what if I wanted to use 30 degrees or 5 degree instead.I have look on the internet for some advice but don't seem to be able to find some?

2. Jan 27, 2013

### Simon Bridge

What's wrong with just putting the different angle in for theta?
http://en.wikipedia.org/wiki/Rotation_matrix

eg. to rotate 30 degrees, sin(30)=1/2 and cos(30)=√3/2 so the matrix becomes:

$$\mathbf{A}=\left ( \begin{array}{cc} \sqrt{3}/2 & -1/2 \\ 1/2 & \sqrt{3}/2 \end{array}\right )$$