Question

how do I use matrices to rotate vectors? I'll fan and medal!!!!!

Answer 1

@SolomonZelman @dan815 @Data_LG2 @iambatman

Answer 2

@bibby @EclipsedStar @bohotness @iGreen

Answer 3

This might help... http://en.wikipedia.org/wiki/Rotation_matrix

Answer 4

that really confused me

Answer 5

@SolomonZelman

Answer 6

well logically we want to add one angle to another right?

Answer 7

recall the idenitites:

cos(a+b) = cos(a) cos(b) - sin(a) sin(b)
sin(a+b) = sin(a) cos(b) + cos(a) sin(b)

now we can use some other identities to turn this into a rotation matrix

x = cos(a) ; x' = cos(a+b)
y = sin(a) ; y' = sin(a+b)

replace the appropriate parts

x' = x cos(b) - y sin(b)
y' = y cos(b) + x sin(b)


we can rewrite the y' so it lines up the x y parts into a more matrix configuration

x' = x cos(b) - y sin(b)
y' = x sin(b) + y cos(b)

notice how this can form the matrix setup:
\[\begin{pmatrix}
\cos(b)&-\sin(b)\\
\sin(b)&\cos(b)
\end{pmatrix}
\binom{x}{y}=
\binom{x'}{y'}\]

Answer 8

I'm so lost..

Answer 9

well, good luck with it then. i dont know how to read minds so i dont know what it is your lost on .

Answer 10

If you want the most basic rotations and transformations, they are gone over here:
http://people.bath.ac.uk/sej20/transform.html