How can I remember how to differentiate and integrate cos and sin?

I find it is best whenever you open your maths paper to draw this diagram to help you remember: Sin(X) -> cos(X)-> -sin(X) -> -cos(X)----->
{Drawn in a circle on the board}
To differentiate you follow the circle clockwise from sine you get cosine but when you differentiate cosine there is a sign change and we get minus sine.
Also it is important to remember that if there is a coefficient, like:
Y= Cos(2x)
We have to times by this when we differentiate and divide by it when we integrate:
dY/DX= 2cos(2x) Integral(Y) = 1/2 cos(2x).
{Symbols drawn on board}
Shall we try some examples?