Rotation of Rectangular Co-ordinates ( X-Y plane about Z-axis )

 X - Y Rectangular Co-Ordinates x= y= Angle of Rotation (z in degree)  = Find  in  X1 - Y1 Rectangular Co-Ordinates Angle of Rotation (angle Z in Radian) Rotation Matrix  K = (k11) (k12) k11=cosz; k12=sinz;k21=-sinz;k22=cosz (k21) (k22) Determinant & Trace x1 (xcosz+ysinz) = y1 (-xsinz+ycosz) = Length in X-Y Length in X1-Y1 Polar Co-ordinate r= √( x2 + y2 ) Polar Co-ordinate φ (in radian) = tan-1 (y/x) Polar Co-ordinate φ (in degree) Rotation Matrix Kp (polar to  polar co-ordinates) = (kp11) (kp12) (kp11=1; kp12=0; kp21=0 ; kp22=1-  (z/φ) (kp21) (kp22) Determinant & Trace r1(r1=r) φ1in radian(φ1=z-φ) φ1in degree Transformation Matrix kpk from Polar Co-ordinate (r1, φ1 ) to Rectangular Co-ordinate (x1.y1) (kpr11) (kpr12) kpr11=cosφ1 ; kpr12=0;kpr21=sinφ1; kpr22=0 (kpr21) (kpr22) Determinant & Trace x1= y1= Transformation Matrix kpp from Rectangular Co-ordinate ( x,y) to Polar  Co-ordinate (r, φ) (kpp11) (kpp12) kpp11=√( x2 + y2 ) / x ; kpp12=0 ;kpp21=0; kpp22=(1/y)*tan-1 (y/x) (kpp21) (kpp22) Determinant & Trace r = φ = Overall transformation Matrix:(x,y) to (x1,y1) (ot11) (ot12) ot11=cos(z-φ)*√( x2 + y2 ) / x  = kpr11*kpp11 ; ot12=0; ot21=sin(z-φ)*√( x2 + y2 ) / x =kpr21*kpp11; ot22=0; ot=kpk*kp*kpp (ot21) (ot22) Determinant & Trace x1= y1= link