I am not yet up to speed
It is just clearer when you know what arc tan is and then why it relates
just briefly in between the J
Not a lot of philosophy
orthogonal vectors briefly:
i,j,k are orthogonal and can be represented as [1 0 0],[0 1 0],[0 0
1] or represent the x,y,z where z is imaginary or you can exclude
imaginary and talk about x and y as orthogonal. These vectors are at
right angles. etc.
I can look up more and try to catch a thread of what you are
comparing and provide some narrative.
Donna
[EMAIL PROTECTED]
On 30-Jun-06, at 6:27 PM, John Randall wrote:
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
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