Transformation of Coordinates 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