Deducir la Matriz de Rotación 2D y Encontrar Ayuda

[Zipi Damn]

I was trying to deduce the 2D Rotation Matrix and I got frustrated. So, I found this article: Ampliación del Sólido Rígido/ (in Spanish).

I don't understand the second line. How does he separate the matrix in two different parts?
Thanks for your time.

 

[traxter]

Hi

In the matrix product in the second line, the vector (cos(sigma + phi), sin(sigma+phi)) should be (cos(sigma), sin(sigma)), which when multiplied by R is by definition (x,y).

Hope this helps.

 

[Zipi Damn]

I don't know why he uses cos(σ+ψ) and sin(σ+ψ) instead of cos(σ) and sin(σ) when the matrix of the second line is separated.

That would make cos(σ+ψ)=cos(σ). Is this true? I can't see that relation. Because there is no similarity between the triangles formed by the vector (x,y) and the vector (x',y'). So it's imposible the cosine is the same.

 

[traxter]

I think it's just a mistake to be honest. It's definitely not true that cos(sigma + phi)=cos(sigma) for all values of these variables, so I think it's safe to assume it's just a mistake.

 

[Zipi Damn]

I think it's just a mistake to be honest. It's definitely not true that cos(sigma + phi)=cos(sigma) for all values of these variables, so I think it's safe to assume it's just a mistake.

Yes, it seems to be a mistake. But this mistake has helped me to analize better these concepts.
Anyway, thank you!