Some trig and geometry is definitely useful—but it's quite limited to be honest. For most things you can use existing algebra libraries and for most things someone else has figured it out before!
The other part that’ll catch you pretty hard if you don’t have strong trig and linear algebra going for you is that debugging is going to be really hard. I admittedly have been deep in positioning-and-attitude control for 5 years now, but the ability to look at a transformation matrix or quaternion and mentally grok exactly what it means odd going to be incredibly useful when you’re trying to figure out why your system isn’t doing what you think it should be.
My calculus is strongest; I can deal with that basically. My geometry is so poor that I am surprised I passed my maths A level.
These books excite me because they give back that, er, constructivist thing that has always appealed to me -- Piaget, Papert, Minsky.
I enjoyed your article, thank you for writing it.
My grasp of trig has relapsed to 13-year-old level. It's an embarrassment!