How Do You Determine the Correct Phase Constant for a Wave?

[grassstrip1]

Homework Statement

I've attached the question where the graph can be found.
Essentially I have no problem determining A=0.04M K= 10π rad/m λ=0.2M ω=π/5 rad/s
I'm having trouble choosing what ø should be.

Homework Equations

y(x,t)= 0.04sin(10πx - π/5t +ø)

The Attempt at a Solution

Since the graph is for the particle at x=0 and t=0 and y=0
0=0.04sin(ø) solving for ø gives π, -π and 0

To try and determine the right phase constant I took the partial derivative to find the transverse velocity.
v(x,t)= (0.04)(-π/5)cos(10πx - π/5t +ø)
Since the particle has a positive velocity at t=1 , plugging in t=1 should give a positive velocity
Therefore ø can't = 0 since using 0 as a phase constant gives a negative velocity for t=1 and x=0
Problem is both plus and minus pi give the right velocity and I'm not sure how to pick the correct one. The correct answer is +π
I'd like to know in general as well how to pick the correct value. Thanks!
http://imageshack.com/a/img547/3680/2tjw.png

 

[BvU]

You did it just right. Many (me too) intuitively fill in $\phi$=0. But if you draw a sin(x), and pull it to the right, you see x=0 is moving down.

 

[grassstrip1]

Okay thank you! I'm just wondering how you can tell the answer is positive pi and not negative since both would give the same sign for velocity

 

[nasu]

It does not make any difference if you pick ∏ or -∏.
cos(a+∏)=cos(a-∏)=-cos(a)