Question on waves: URGENT please!!! thanks in advance?

[3]

The drawing shows a snapshot of a transverse wave traveling along a string at 7.9 m/s. The equation for the wave is y(x, t) = A cos (wt + kx).<br />
http//tinypic.com/view.php?pic=2irlmp3&s=3<br />
<br />
A = 2<br />
w = 1240.9<br />
k = 157.08<br />
At what times could this snapshot have been taken? (Give the three smallest nonnegative possibilities in order.)<br />

 

[answer_man]

For x=0, y=0 so we have

y(0,t) = A cos(wt + k*0)

y(0,t) = A cos (wt) = 0

So cos(wt) = 0

Since the zero crossing of the cosine (at x = 0) is going from + to - the "wt" must be either Pi/2 or or that plus some multiple of 2*Pi

wt = Pi/2 + n*2*Pi (n=0,1,2,...)

t = (Pi/2)(1 + 4*n)/w (n=0,1,2,...)

The three smallest 'n's give the three smallest 't's