Transformation ofCoordinates Under Rotation around Z-axis ( x, y ) --> (x1, y1 ) Rotation Angle--( +) if Anti ClockWise Rotation     ( -) if ClockWise Rotation Enter Value(x-y frame) of Vector A i + j Enter Angle of Rotation in Degree (+) ( -) Find Angle in Radian Find Value(x1-y1 frame) of Vector A i1 + j1 Value(x1-y1 frame) of Vector A( negative angle) i1 + j1 Find Value(x1-y1 frame) of Unit Vector i1 i + j Find Value(x1-y1 frame) of Unit Vector j1 i + j Value(x1-y1 frame) of Unit Vector i1(negative angle) i + j Value(x1-y1 frame) of Unit Vector j1(negative angle) i + j Find Magnitude Of A in x-y x'-y' Find Angle Of A with axis x x1 (+angle) Find Value of Rotation Operator a11 a12 (x,y)->(x',y')Matrix Form(2x2) a21 a22 (- angle) Find Value of Rotation Operator a'11 a'12 (x',y')->(x,y)Matrix Form(2x2) a'21 a'22 sin of Angle cos of Angle
In X-Y Frame, A = xi +yj
In X'-Y' Frame, A' = x' i' +y'j'
If Angle of Rotation is K in Anti ClockWise Direction ( taken as + )
i' = i cos K + j sin K
j' =- i sin K + j cos K
or [ i' , j' ] =[ cos k sin K ] [ i ]
[ -sin K cos k ] [ j ]
or [i' , j' ] = R [i ]
[j ]
where R is rotation operator.
For Angle of Rotation K in ClockWise Direction ( taken as - )
[i' , j' ] = R' [ i]
[ j]
where R' =[ cosk -sink ]
[ sink cosk ]
Similarly [x' , y' ] = R [ x ]
[ y ]
for (+) Angle of Rotation
and [x' , y' ] = R' [ x ]
[ y ]
for (-) Angle of Rotation
( i , j ) --> ( i' , j' ) are called Base or Basis Vector transformation under Rotation. sin ( -k ) = - sin k
cos( - k ) = cos k