 Then, in the "x'y'" system, "P" will have polar coordinates formula_5.Using trigonometric functions, we have

and using the standard trigonometric formulae for differences, we have

Substituting equations () and () into equations () and (), we obtain

Equations () and () can be represented in matrix form as

which is the standard matrix equation of a rotation of axes in two dimensions.The inverse transformation is

or

Find the coordinates of the point formula_8 after the axes have been rotated through the angle formula_9, or 30°.