Defining Amplitude and Angle for Differential Equation x(t) = Asin(Wt + z)

[Dissonance in E]

Homework Statement

x(t) = Asin (Wt + z)
Define values for A(amplitude) and z(angle) so that:
x(0) = x0 and x´(0) = v0

Homework Equations

Chain rule.

The Attempt at a Solution

Im pretty sure I got the z part right:
x(0) = Asin(z) = x0
x´(0) = AWcos(z) = v0

Solve simultaneous equations for z:

sin(z)/cos(z) = (x0/a)(AW/v0)
tan(z) = (x0W/v0)
z = tan^-1(x0W/v0)

As for the A part I have no idea how to go about solving it:

Rearranging the x(0) equations for A
Asin(z) = x0
AWcos(z) = v0
A=x0/sin(z)
A=v0/Wcos(z)

Now what?

 

[Mark44]

Substitute the value you got for z into the equation A sin z = x₀. That will give you A sin(tan^-1(x₀W/v₀) = x₀. Then solve that equation for A, which will give you A in terms of x₀, v₀, and W.