The only problem is that you applied the wrong formula ^^
and you used ?
And don't forget x=-1, not 1.
As for the matter of learning these formulae or not... I don't think it's something you have to know by heart. Your reasoning is perfect. You just have to be careful with the domain of the inverses. I guess it would be enough to know it (and of course, to know how to use the unit circle, but this is a mandatory condition)... See how you thought you were wrong ?