Derivative of arccos (+ feedback :D)

So I posted a lot of questions last night and this morning, I want to say thanks to all those who helped me. I am just back from the exam and yes most of the advice I got from you all was relevant to what came up in it... I believe I will have passed well ONLY because of the advice I got on here. One night of topic questions on here and I learn WAY more than one whole year of university tuition... well that's another rant for another day :) But anyway the point I want to make and the question I want to ask is:

Last night I asked for help on $\displaystyle y=arctan(x)$ and finding $\displaystyle \frac{dy}{dx}$. In this exam, the similar thing came up this time $\displaystyle y=arccos(x)$. It is the only question I did not know and I should have been prepared for this... but, I could not find a substitution like the one used for the arctan. Now please somebody tell me what I can do once I get to $\displaystyle \frac{-1}{sin(y)}$, remember that $\displaystyle x=cos(y)$ this time and I had to find something, I think, to link sin and cos, but I couldn't do it? I know you can't just square them otherwise its easy...