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...

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 a point (x,y)∈R2(x,y)∈R2 around the origin through angle tt, then f(x,y)f(x,y) is the result.

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

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milcah answered 8 months ago

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