Parableman explains the close association between these two concepts. They really are the foundation of the Christian gospel. To me, to repent is to change your mind and your direction in order to think different things about God, and trust him alone for your salvation. It involves changing the very core of your being in such a way that the direction of your life has changed. If faith is not worked out in life it isn’t faith at all.
As someone once said, it is faith alone that saves, but the faith which saves is never alone.
Of course the danger of this is that we misunderstand the way in which our faith is worked out. We can become like the Galatians who began with the Spirit and ended in the flesh. We must daily cast ourself not on our own ability to ‘be a good Christian’ but rather on the ability of Jesus’ work on the cross to defeat sin in our lives.
We can all too easily be thrown by the latest sin we notice in ourselves (or for that matter someone else!) Guess what, we make mistakes but as the line in the song goes “Because its grace-theres nothing I can do to make you love me more, to make you love me less than you do”
It seems that us Christians will spend our entire lives like jollyblogger still trying to get the gospel.