# Deducir la Matriz de Rotación 2D y Encontrar Ayuda

• Zipi Damn
In summary, the conversation discusses the use of cos(σ+ψ) and sin(σ+ψ) instead of cos(σ) and sin(σ) in a matrix product, which is believed to be a mistake. The person who found the article thanks the others for their time and mentions that the mistake helped them better understand the concepts.
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?

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.

1 person
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.

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.

traxter said:
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!

## 1. How do I deduce the rotation matrix in 2D?

In order to deduce the rotation matrix in 2D, you need to first identify the angle of rotation and the direction of rotation. Then, you can use the following formula to calculate the rotation matrix:

cosθ -sinθ
sinθ cosθ

Where θ is the angle of rotation in radians.

## 2. What is the purpose of the rotation matrix in 2D?

The rotation matrix in 2D is used to represent and perform rotations on 2D objects. It is a mathematical tool that helps to describe the orientation and position of an object after a rotation has been applied to it.

## 3. How does the rotation matrix affect the position of points in a 2D object?

The rotation matrix affects the position of points in a 2D object by rotating them around the origin point by the specified angle and direction. This means that the coordinates of each point will change according to the rotation matrix, resulting in a new position for the object.

## 4. Are there any other methods to find help with deducing the rotation matrix in 2D?

Yes, there are various resources available online such as tutorials, videos, and forums that can provide assistance in deducing the rotation matrix in 2D. Additionally, seeking help from a math or physics teacher or consulting a textbook can also be helpful.

## 5. Can the rotation matrix be used for 3D rotations as well?

No, the rotation matrix in 2D is specifically designed for 2D rotations and cannot be directly applied to 3D rotations. However, a similar concept called the rotation matrix in 3D can be used for 3D rotations, which involves a 3x3 matrix instead of the 2x2 matrix used in 2D.

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