Equations for one-axis tracking surfaces

Hello,

I am doing some work trying to model tracker geometry for one-axis trackers with tilted axes. I looked at the "SAM photovoltaic model technical reference" section 5.3 (page 20) and have a few questions about this:
-Before equation (5.6), you have a=sin(theta)/sin(beta). Should (beta) be replace by (beta_s), the surface tilt angle derived above? If not, what is beta?

-I am trying to check equation (5.6). I looked at the case of a horizontal East-West tracker. For such a tracker beta_s is simply equal to theta, so "a=sin(theta)/sin(beta_s)" is equal to one, I think (assume beta should be relaced by beta_s above equation (5.6).

But then from equation 5.6 we get gamma_s=gamma_0+arcsin(1)=gamma_0+pi/2. Whereas I would expect there to be two solutions, one with gamma_0+pi/2, one with gamma_0-pi/2 (depending which direction the tracker is facing - eg a horizontal East-West tracker would have one azimuth before solar noon, and a different azimuth after solar noon).

Any thoughts about this?

Best regards,
Sophie

In response to my own question, I now realize that in equation 5.5, when a=cos(theta), beta_s can be either +theta or -theta, so for equation 5.6, a=sin(theta)/sin(beta_s) can be either +1 or -1, which then gives the two angles I was looking for.