Let (x, y) be the co-ordinates of a point P referred to a set of rectangular axes OX, OY. Then its co-ordinates (x′,y′) referred to OX′, OY′, obtained by rotating the former axes through an angle θ are given byx′=xcos⁡{θ}+ysin⁡{θ}y′=−xsin⁡{θ}+ycos⁡{θ}How do we derive the result for (x′, y′) from (x, y) ?

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Let (x, y) be the co-ordinates of a point P referred to a set of rectangular axes OX, OY. Then its co-ordinates (x′,y′) referred to OX′, OY′, obtained by rotating the former axes through an angle θ are given byx′=xcos⁡{θ}+ysin⁡{θ}y′=−xsin⁡{θ}+ycos⁡{θ}How do we derive the result for (x′, y′) from (x, y) ?

Nevaeh Jensen · Accepted Answer

Step 1Let Aθ the matrix of the rotation transformation:Aθ=(cos⁡θ−sin⁡θsin⁡θcos⁡θ)so if u=(x, y)T and u′=(x′, y′)T is the vector obtained by rotating the vector u by an angle θ thenu′=Aθ×u

Micah May · Accepted Answer

Step 1  If Aθ is the matrix of the rotation transformation:  Then,  Aθ=(cos⁡θsin⁡θ−sin⁡θcos⁡θ)  ((begin{matrix}x^{}

Let (x, y) be the co-ordinates of a point P referred to a set of rectangular axes OX, OY. Then its c

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