dly wrote: > I think all these inter-relationships would be much clearer if you > talked about polar notation, orthogonal vectors, complex numbers and > what trigonometric functions actually are. >
I think that trigonometric functions are best defined by solutions to initial value problems, for example, cos is the unique solution to the IVP y''+y=0, y(0)=1, y'(0)=0requires more preliminaries or equivalently as a series. Measuring a length along a curve (as in the unit circle definition) has some serious difficulties that are glossed over in elementary courses. I'll leave the question of the trigonometric functions actually are to the philosophers. I was using polar notation for complex numbers in my discussion of ^. _1: this was so that you could get the roots using Euler's formula. Obviously complex numbers can be viewed in many ways. Where do orthogonal vectors come in here? If you have a clearer explanation, please post it. I am just explaining it the way I understand it. Best wishes, John ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
