RedCrab Math Tutorial
 

Matrices and Rotation

A polar coordinate can be described by a pair of numbers (x, y). The numbers are the distance of A from the y axis (x), and from the x axis (y) in the coordinate system. Any points to the left of the y-axis will have a negative x coordinate. Any points below the x axis, will have a negative y coordinate.

   

 
Instead with the term (x, y), we can describe the point with radius r and the angle θ (r, θ).





In the diagram above, r is the hypotenuse of a right-angled triangle
 
The x-position can be calculated from the radius r and the angle θ according to the following formula:
The y-position is calculated accordingly from the formula:

 
In the following figure, we have rotated the point (x, y) by the angle φ. So, we have now:

 
For the following trigonometric equation


we can write


and we become


   

 
When we write this in a matrix form it looks like this

 
The example below shows a matrix that rotates the vector by an angle of φ = 30 °.

 
With this Matrix the position vector for the point (1,0) becomes

 
Calculation and graphical representation in RedCrab Calculator

 
A rotation in 3-space, counter clockwise through the angle φ about the z-axis shows the matrix below

 
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Matrices Definition
Matrices Calculation
Matrices & Simultaneous Equations
Matrices Determinants
Row Operations of Matrices
Matrices and Geometry, Reflection
Matrices and Geometry, Rotation
 
   


           
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