how is the relationship between the central angle theta and the depth of an amount of liquid in a cylinder tank on its side h= r(1-cos(theta/2)?
Central Angle and Depth Relation Calculus
The picture might help: http://i6.photobucket.com/albums/y234/Agent_0_Smith/tankonitsside_zps904c9330.jpg
cos(α/2) = (r-h)/r
r*cos(α/2) = r-h
h = r - r*cos(α/2) = r(1 - cos(α/2))
h = r(1 - cos(α/2))
Hopefully that helps.
Your formula h= r(1-cos(theta/2) is correct if the liquid level is below the center of the tank.
If the liquid level is above the center of the tank, the formula should be h= r(1+cos(theta/2)