I have a data set where one of the variables is in polar coordinates ($\varphi$ = 0° to 360° degrees) and PCA was applied in order to reduce dimensions.
As far as I know, using PCA on polar coordinates does not make sense from a mathematical point of view, because 0° and 360° would be treated as completely opposite values, although being essentially the same (am I right?)
What would be the optimal approach to using PCA on such a data set with mixed types of variables including polar coordinates?
What I thought of is transforming polar coordinates to Cartesian coordinates (assuming $r = 1$): $x = cos \varphi$ and $y = sin \varphi$ and weighting these new variables by 0.5. Is this solution mathematically correct? Are there any other suggestions to solve this?