For the trig function issue, you can always define new functions like "cosr(x) = cos(radToDeg(x))". That could help take off some of the "cognitive load" (roughly, the things you have to keep track of). I haven't heard of hyperbolic trig functions taking degrees but I suppose it happens....

What do you mean by "close enough"? For instance, what value of "a" does your Newton's Method give for s=10, h=5, d=3?