I have posted at my personal web page http://web.maths.unsw.edu.au/~norman/Rational1.htm some short pdf papers that might interest teachers of trigonometry. One is called `The Wrong Trigonometry', one is `A Rational Approach to Trigonometry', and another is `Survivor: The Trigonometry Challenge'.
These short papers, meant for a high school audience, discuss a simpler form of trigonometry that students can learn in a fraction of the time required for the usual trig. The idea is to work exclusively with ratios, hence the name `Rational Trigonometry'. There are five main laws that replace the usual cosine , sine laws etc, and calculators/tables turn out not to be needed (although they are still helpful). I would be interested in examples of standard trig problems that people think might not be solvable with this new methodology.