This is a question from GCSE level, so please offer a simple explanation if possible.
I have been given the following:
To rotate a point (x,y) 90deg anti-clockwise, pre-multiply the x y matrix with:
Similarly, for a an anti-clockwise rotation of 180deg, it's:Code:( 0 -1 ) 1 0
p.s., how can I create a matrix in this forum in the math tag?Code:-1 0 0 -1
It's tough to remember so memorize so many matrices when there are very similar looking matrices for reflection (on x axis, y axis and y = -x). I think perhaps, an explanation of how these matrices are created will help me. Or maybe some pointers on how to memorize at least 8-9 such matrices.
Find theta and hence the angle of rotation and the direction of
top row of matrix (-1/√2) (1/√2)
bottom row (-1/√2) (-1/√2)
Clockwise direction but
when you calculate arccos (-1/√2) you get 135 deg which is correct but
arcsin (-1/√2) is -45 deg
What am I missing?
Thank you for your reply and I understand where the -135 deg comes from. Its negative due to being a clockwise rotation about the origin (anti clockwise it is 225 deg as you say), where I am getting lost is why do I get -45 deg for calculating arcsin (-1/√2) ?