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# FP1 OCR: 'what matrix represents rotation thru angle x clockwise about the origin?

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im trying to teach myself FM and im really struggling with resources and theres a concept in chapter 1 that im really not getting

i think its meant to help you understand a generalised rule about how to get a transformation matrix of any rotation around the origin using trig. but im very confused and ALSO i dont actually know how much i should be dwelling on this? at first i hoped it wasnt a crucial concept, just a note that we wouldnt be tested on. i feel like this was wishful thinking though since there are actually questions about it later in the exercises.
Attachment 521053521055

soo thats the concept.. and i just dont get it? i cant do the thing where you work out whether cosx and sinx will be positive or negative for each rotation. if you dont know how to explain or cant be bothered does anyone at least kjnow how useful this is to know, or any other resources that explain it? i cant find any

thanks
Attached Images

2. (Original post by EmergencyBagels)
im trying to teach myself FM and im really struggling with resources and theres a concept in chapter 1 that im really not getting

i think its meant to help you understand a generalised rule about how to get a transformation matrix of any rotation around the origin using trig. but im very confused and ALSO i dont actually know how much i should be dwelling on this? at first i hoped it wasnt a crucial concept, just a note that we wouldnt be tested on. i feel like this was wishful thinking though since there are actually questions about it later in the exercises.
Attachment 521053521055

soo thats the concept.. and i just dont get it? i cant do the thing where you work out whether cosx and sinx will be positive or negative for each rotation. if you dont know how to explain or cant be bothered does anyone at least kjnow how useful this is to know, or any other resources that explain it? i cant find any

thanks
A rotation by theta clockwise = a rotation by -theta anticlockwise, so put -theta into the matrix, then use the fact that cos(-theta) = cos(theta) and sin(-theta) = -sin(theta) to simplify.

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