Matrice question about how rotation effects graphs. Easy question

Question

anonymous · Answer

attachment

dumbcow · Answer

use angle sum identity for sin and cos

cos(a+b) = cos(a)cos(b) - sin(a)sin(b)
sin(a+b) = sin(a)cos(b) + sin(b)cos(a)

where a = theta_1  and b=theta

anonymous · Answer

does it mean the vector arrow goes closer to the y bar?

dumbcow · Answer

yes, vector rotates counter-clockwise so toward y-axis

anonymous · Answer

ah yeh i know that

dumbcow · Answer

matrix R must be a 2 by 2 matrix
when you multiply R by [acos   asin]  you should end up with what i posted above

dumbcow · Answer

or just look at solution here :) http://en.wikipedia.org/wiki/Rotation_matrix

anonymous · Answer

wow awesome...i thought the question was too simple that it wouldn't be put on the web...just needed to visualise it to make sure