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  3. f(x,y)=(xcos(t)?ysin(t),xsin(t)+ycos(t))f(x,y)=(xc

f(x,y)=(xcos(t)?ysin(t),xsin(t)+ycos(t))f(x,y)=(xcos?(t)?ysin?(t),xsin?(t)+ycos?(t)) defines rotation around the origin through angle tt in the Cartesian plane R2R2. If one rotates...

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Basic Math

f(x,y)=(xcos(t)?ysin(t),xsin(t)+ycos(t))f(x,y)=(xcos?(t)?ysin?(t),xsin?(t)+ycos?(t))

defines rotation around the origin through angle tt in theCartesian plane R2R2. If one rotates a point (x,y)?R2(x,y)?R2around the origin through angle tt, then f(x,y)f(x,y) is theresult.

Let (a,b)?R2(a,b)?R2 be an arbitrary point. Find a formula forthe function gg that rotates each point (x,y)(x,y) around the point(a,b)(a,b) through angle tt.

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