General rotation matrix

In the chapter ‘matrix transformations about the origin’, we learned how to represent common rotations (i.e. 90 and 180 degrees) about the origin.

Here, we’ll learn how to represent a rotation of any angle.

Note: because all matrix transformations must keep the origin at, well, the origin. This means that our centre of rotation is always (0,0) when working with matrix transformations.

General rotation matrix

A rotation anticlockwise by \theta degrees (an angle) can be written as a matrix tranformation:

\begin{pmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{pmatrix}

flashcards

QuestionAnswer
What is the centre of rotation for all matrix transformations?(0,0), because matrix transformations must keep the origin at the origin.
What matrix represents an anticlockwise rotation by \theta degrees about the origin?\begin{pmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{pmatrix}