Look here.
Let be the rotation in the plane through angle in the anti-clockwise direction. Find the matrix which represents the linear transformation .
Not too sure how to start this question off. The only thing I can think of doing for this is to use complex numbers.
If someone could give me a clue on how to start off this question and I'll try and do it myself.
As to why rotation through angle is given by
look at what it does to the "basis vectors"
That is, (1, 0) is mapped to the point . The distance from (0, 0) to that point is and that point lies along a line with slope . Since the slope of a line is the tangent of the angle the line makes with the x-axis, that says that (1, 0) has been mapped to a point on the line that makes angle with the x-axis. That is, it has been rotated through angle .
tells us the same thing.