The armature of an AC generator has 90.0 rectangular loops each measuring 8.00cm by 12.0cm; the generator has a sinusoidal voltage output with an amplitude of 24.0V. If the magnetic field of the generator is 0.250T, with what frequency does the armature turn?

I tried solving this with:

E=wNBA*sin(theta)

I come up with 111.111s^-1 but the listed answer is 17.7s^-1.

Could someone help me with what I might be missing?

I come up with 111.111s^-1
That value is w = 2*pi*f.
Now find f.

Hi there,
I just went through the calculation and I get a radial frequency of 111.111 rad/sec. Radial frequency is the rotational frequency of the armerature in this case. That is how many times per second does the thing rotate.
Frequency is a measure of how many times per second something periodic repeats itself. So the actual frequency is the radial frequency divided by 2pi. If you take the 111.111rad/sec and divide it by 2pi you get 17.7 s^-1.
I'm basically just adding a little to the previous reply, as that person got it right on the nose, so to speak.
Many Smiles,
Craig