Simple Harmonic Motion - Conflicting equations

[jumbogala]

Homework Statement

What is the equation for the displacement of a sin wave (eg something in SHM)?

My book says x(t) = Acos(ωt + ɸ₀)

My prof's notes say y(x,t) = Asin(ωt - kx + ɸ₀)

Homework Equations

The Attempt at a Solution

I'm not confused about why one is sin and the other is cos. I'm confused why one has the extra term -kx. When do you use which?

I have a question that asks me to write the displacement for a sine wave traveling to the left with frequency 200 Hz, speed 400 m/s, amplitude 0.010 m, and initial phase 90 degrees. So I'm not sure which of the above to use.

 

[rl.bhat]

First one is the general equation of SHM.
The second one the equation of the sine wave propagating in a medium towards the positive x direction.
You have to use the second equation to find the displacement with a small modification.