DIFFEQ An object attached to an elastic spring executes simple harmonic motion.

The natural frequency of the motion is 1 cycle/second and the amplitude is 1ft. Find the velocity of the object as it passes the point x= 6 inches moving upward. Hint: use the alternate form.
So I know I will be using Asin(wt+theta)
f=1 so w=2pif so w=2pi
and I know the amplitude...
I dont know where to go from here to find the phase angle

A = amplitude = 1 ft
f = frequency = 1 Hz

The general equation for position of SHM is:
x = A sin(ωt + θ)

The general equation for velocity of SHM is given by the first derivative of x:
v = dx/dt
v = A ω cos(ωt + θ)

The angular velocity is:
ω = 2π f
ω = (2π rad) × (1 Hz)
ω = 2π rad/s

Nothing is given about the position or velocity at a particular time and nothing is asked for at a particular TIME (they only ask for something at a particular displacement), so you can choose the position to be x=0 at time t=0, which means that
θ = 0 rad

So your equations become:
x = sin(2π t)
v = 2π cos(2π t)

Now, find the time at which x = (6 in) = (0.5 ft)
0.5 = sin(2π t)

so . . . . . . . . . . . . . . . . . . . . . . . . . . see note below

2π t = π/6
or
2π t = π - π/6 = 5π/6

t = 1/12 s
or
t = 5/12 s

Enter that time into the equation for velocity.

v = 2π cos(2π × 1/12)
v = π√3 ≈ 5.44 ft/s

or

v = 2π cos(2π × 5/12)
v = -π√3 ≈ -5.44 ft/s

As you want it to be moving upward, the only valid solution is:

v = 5.44 ft/s < - - - - - - - - -answer

Have a look at the graph:
http://oi45.tinypic.com/2zp4eig.jpg

Note:
remember that sin(α) = sin(π - α)
and put your calculator in RAD modus