Position vs time graph simple harmonic motion phase constant

[Ly444999]

Homework Statement

http://imgur.com/a/FDfAp

What is the phase constant?

Homework Equations

x(t) = A*cos(ωt+Φ)

The Attempt at a Solution

If I'm not mistaken at t = 0 the graph starts at half the amplitude or 5. Also the amplitude of this graph is 10, and at t = 0 angular velocity is also 0.
5 = 10*cos(0 + Φ)
Φ = arccos(5/10)
Φ = π/3
The answer is supposed to be -2π/3, I'm not sure what I did wrong or if I'm even doing the question right.

 

[ehild]

Homework Statement

http://imgur.com/a/FDfAp
What is the phase constant?

Homework Equations

x(t) = A*cos(ωt+Φ)

The Attempt at a Solution

If I'm not mistaken at t = 0 the graph starts at half the amplitude or 5. Also the amplitude of this graph is 10, and at t = 0 angular velocity is also 0.
5 = 10*cos(0 + Φ)
Φ = arccos(5/10)
Φ = π/3
The answer is supposed to be -2π/3, I'm not sure what I did wrong or if I'm even doing the question right.

The phase constant is different if you suppose x(t) as x(t) = A*cos(ωt+Φ) or x(t) = A*cos(ωt-Φ) or x(t) = A*sin(ωt+Φ), x(t) = A*sin(ωt-Φ).
You also have to take into account if the function increases or decreases at t=0. The function in question increases, so the phase can not be pi/3. But it does not mean that -2pi/3 is correct.

 

[haruspex]

5 = 10*cos(0 + Φ)
Φ = arccos(5/10)

The arccos function is defined to return a value in a certain range, but there are infinitely many solutions to cos(Φ)=0.5.
What other solutions are there in, say, (-π, π), or (0, 2π) if you prefer?
These all give the right value at t=0, but what about an instant later?