ray I have been absorbing your thoughts for a few days now and have read that many times, i have always associated maths with pictures, sketches, drawings, graphs, algebra, chalk marks on the floor, scribbles on the backs of cigarette boxes, full-scale drawings, weird rabattements that no one ever understood or even believed were real, perhaps it's more to do with the impact that maths has on our personal lives, i recall getting up late and needing to be at an airport 60 miles away in one hour, the realisation that i would need to start getting beyond 92 miles per hour quickly set in, the mean value theorem very nearly cost me my life that day, i always associate it with being late, or motorway carnage, i could draw it i guess but it also represents a multitude of other things, it's funny how we " see" things, objects, situations every moment of every day yet find it hard to represent them in a true way, be it personal or otherwise, i am still none the wiser as to mathematical expressions, in the new year i will be attempting to show how to represent simple structures in plan, elevation and auxiliary plain, i want to show how to abstract from the drawing completely with the idea of cosines, i have attempted to show how to do this many times with absolutely no success whatsoever, there doesn't seem to be a graspable stepping stone between a drawing and the concept of a cosine, the concept of rise over run is never an issue, i don't refer to it as a tangent as this word is too confusing and sin's don't need to be mentioned either, ray i do appreciate that this sounds like a simple problem but it is not, measuring from auxiliary planes is simply not acceptable as we will be constructing real parts to a real building, i need some kind of way of " seeing" them on the drawing, i have learnt that people understand right angled triangle but fail to understand an auxiliary plain, then of course there is the concept of" angle who's cosine is" which seems to fly in the face of the first understanding, it may be simple to you and i ray but these two concepts are completely irreconcilable with each other in the mind of someone who has never met these ideas, the students have learning difficulties and very low levels of concentration, there is no way i can start waffling on about some circle such that, ultimately we will be drawing wood working joints with solid angles on them for cutting, i read somewhere that maths is the art of giving the same name to completely different things, cosine is a ridiculous word, it sounds puzzling to begin with, i need a new word for it, preferably which begins with cos and i need a word for it's argument, they are going to have to press that button on the calculator at some stage and it's argument has to have some relevance to the appearance of the index notation that will appear on the calculator, it just simply has to make sense ray, i must apologise for my word rabattement, apparently it isn't a word, perhaps i could use cos as a pneumonic? or the beginning of another word that describes a pneumonic that says what it does, remembering that the rule needs to explain that multiplying by it and dividing by it is a back and forth conversion, i know I'm asking a lot but i think this is the right place to be asking this question