Sine Wave: The archetypical love story. The couple take some time to warm up to each other and reach their peak, but just as they start to relish the relationship it all comes down rapidly. Better than cosine in the sense that at least the couple end up where they started rather than down in the dumps.
Cosine Wave: The love at first sight story. It starts on a high. Unable to sustain the impetus it goes for a free fall.
Tan wave: The dream love story. It can't get better than this. After a slow start its a case of up, up and away. There is no stopping this wave and as the name reflects, it almost always seems tangential to the actual curve that one is on.
Cosecant wave: Married life maybe?? Marriages, they say, are made in heaven and it is only natural that this wave starts from somewhere there. And then things start degrading and its all downward for a while until it meets the sine wave. Here, realization strikes and efforts are made to make things better. Reward isn't too far away and soon things take a turn for the better and slowly but surely its back to where it all started, heaven.
Secant wave: " You cheated on me!! ". Those seem to be the words of battered half somewhere in the middle of the relationship. How else can you possibly explain the drastic change in the curve? A sudden jolt when the relationship reaches its heights, and in next to no time both of them are staring at the abyss. Despite forgiveness and conscious efforts to make things better it leaves both the parties involved scarred for life.
Cotangent wave: The fling. They came they saw and they captured each other, albeit briefly. Intense at the start it then takes a dramatic downward plunge. Somewhere in the course of the fall, this curve meets its happy cousin, the Tan curve but lessons aren't learnt and the fall continues unhindered.
P.S The above "analysis" has been done considering only one cycle of the curves starting from zero to pi. Detailed analysis considering the curves till infinity would be very similar to the above ones except for the Tangent or the Cotangent curve which maybe equated with the life cycle of a casanova.