In maths, if we practice well with understanding, we will surge forward in our learning, leading the others and gaining valuable knowledge.
However, if we take it easy, trying to buy time and not learning seriously, our maths learning will lag behind others.
In trigonometry, sine waves do perform the same.
If an energetic, excited sinewave is around, it will always lead the pack, staying ahead of the rest.
A lazy sinewave, on the other hand, will struggle to follow, always lagging behind the group.
Diagram 1 A race of sinewaves
From diagram 1, we can see that the winner is obviously the green one.
Assuming the finishing line is the y-axis (vertical line), we can see that the green-coloured sinewave leading the others, followed by the blue sinewave, and the lazy pinkish sinewave lagging at the back.
Another way to view this is to set the blue sinewave as reference (x = 0 second).
The green sinewave has crossed the line (y-axis) 1 second before. ==> Lead
The pink sinewave has yet to reach the y-axis having 1 more second ==> Lag
So do you want to be the enthusiastic green sine wave or the lazy pink sine wave in your maths education?