Question: I have attempted this problem from my homework set, but I cannot manage to get it. Any help is appreciated! 3)Let R be the set

I have attempted this problem from my homework set, but I cannot manage to get it. Any help is appreciated!

3)Let R be the set of all rotations about the origin of the unit solid disk. Such rotations can be represented by matrices

( cos sin)

( sin cos) ,

where denotes the angle of rotation. Prove that R is a group under the composition of rotations. Are there any finite cyclic subgroups of R?

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