Out of Phase Waves: Solving the Relevant Equation

[ravsterphysics]

2. Relevant equation

The Attempt at a Solution

I can see straight away that the waves are 90 degrees out of phase so pie/2.

But how is X ahead of Y? It looks like Y is ahead of X by pie/2.

 

[berkeman]

But how is X ahead of Y? It looks like Y is ahead of X by pie/2.

The horizontal axis is time, so X is oscillating up before Y is oscillating up. Look at the origin -- X is full size, and Y is just starting to move positive from zero... The key is to look at where the two waveforms are at the same time (say t=0) and ask yourself which one is "leading" the other. Makes sense?

 

[haruspex]

Another way to look at it..
"Ahead" means earlier in time. Earlier in the graph is to the left. The X curve is left of the Y curve by one quarter period.