Creating a parametrized ellipse at an angle I'm creating a computer program where I need to calculate the parametrized circumference of an ellipse, like this:
x = r1 * cos(t), y = r2 * sin(t)

Now, say I want this parametrized ellipse to be tilted at an arbitrary angle. How do I go about this? Any obvious simplifications for i.e 30, 45 or 60 degrees? 

If you want to rotate $\theta$ radians, you should use $$t\mapsto \left(
\begin{array}{c}
 a \cos (t) \cos (\theta )-b \sin (t) \sin
   (\theta ) \\
 a \cos (t) \sin (\theta )+b \sin (t) \cos
   (\theta )
\end{array}
\right)
$$
