What is the Difference Between Sinusoidal and Cosinusoidal Wave Equations?

[JoeyAndres]

Homework Statement

This is from the Young and Freedman 13th Ed book, chapter 15 "Mechanical Waves.
It's the same question in the book found in this link:
https://www.physicsforums.com/showthread.php?t=557243

My problem though is much more fundamental I guess. In the part c, the manual suggest (I ran out of hope after 3 hours) that I use y(x, t) = Asin(2π(t/T - x/λ)) +ve direction. What made me confuse is, throughout the book y(x,t) = Acos(2π(x/λ - t/T)). I reckon, its something to do with π phase difference. So what is the difference, can you derive it for me? I just don't know.

Homework Equations

y(x, t) = Asin(2π(t/T - x/λ))
y(x, t) = Acos(2π(x/λ - t/T))

 

[jbsteele]

The Attempt at a Solution These two equations are the same, but with a phase shift of π/2. The equation y(x,t) = Asin(2π(t/T - x/λ)) is shifted by π/2 from y(x,t) = Acos(2π(x/λ - t/T)). This means that the wave represented by y(x,t) = Asin(2π(t/T - x/λ)) will have a maximum value of A at x = 0 and a minimum value of -A at x = λ/2, while the wave represented by y(x,t) = Acos(2π(x/λ - t/T)) will have a maximum value of A at x = λ/2 and a minimum value of -A at x = 0.