How to calculate the orthogonality error between sine and cosine wave?

Question

As the picture below(assume the magnitude is the same),the zero-crossing points of the SIN and COS signals do not occur at the precise distance of 90°.So I want to figure out the φ which is φx-φy. PICTURE1 Through information research,I found that the orthogonality can be calculated out of the magnitude of two 90° angle shifted components.Possible angle combinations are 45° and 135°, 135° and 225°, 225° and 315° or 315° and 45°. And the orthogonality error can be calculated by the equations below: $$ M_{45}=\sqrt{X_{45}^{2}+Y_{45}^{2}} \\ M_{135}=\sqrt{X_{135}{ }^{2}+Y_{135}{ }^{2}} \\ \varphi=2^{*} \arctan \left(\frac{M_{135}-M_{45}}{M_{135}+M_{45}}\right) $$ $$ X_{45}, X_{135}: \quad Cosine~values~at~45^{\circ} ~and ~ 135^{\circ} $$ $$ {Y}_{45},{Y}_{135}: \quad Sine~values~at~45^{\circ} ~ and~ 135^{\circ} $$ I wonder how these equations are derived?