I was trying to prove:
To carry out a rotation using matrices the point $(x, y)$ to be rotated from the angle, $θ$, where $(x′, y′)$ are the co-ordinates of the point after rotation, and the formulae for $x′$ and $y′$ can be seen to be
$x'= x \cosθ - y \sinθ$
$y'= x \sinθ + y \cosθ$
But when I prove it by trig/geometry, it has to be split into obtuse and acute case. Is there a way I could go straight forward without casework?