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But math never decreed that sine and cosine have to take radian arguments!That is not entirely true. It comes from the relationship between those functions and the complex numbers via the Euler formula.
ix
e = cos x + i sin x
There may be arithmetic/numerical inconveniences, but that's not all there is to "math".
Let's define ncos and nsin ("nice cos, nice sin") as follows:
nsin x = sin 2πx
ncos x = cos 2πx
So then what do we make of:
ncos x + i nsin x
This has to be
cos 2πx + i sin 2πx
which is then
2πix ( 2π) ix ix
e = ( e ) = f
2π
Where f = e is a weird number like 535.4916. This f doesn't have nice properties. E.g.:
d x x
- f /= f
dx
Otherwise it works; for instance 90 degrees is 0.25 and surely enough
0.25i
f = i
In situations not involving e in relation to angular representations via Euler, f cannot replace e.
I'm all for having parallel trig functions in libraries that work with turns, though.
The annoying 2π factor shows up in lots of places though. Should way, say, in electronics, redefine a new version of capacitive reactance which doesn't have 2πf in the denominator, but only f?
That is not entirely true. It comes from the relationship between those functions and the complex numbers via the Euler formula.
There may be arithmetic/numerical inconveniences, but that's not all there is to "math".Let's define ncos and nsin ("nice cos, nice sin") as follows:
So then what do we make of: This has to be which is then Where f = e is a weird number like 535.4916. This f doesn't have nice properties. E.g.: Otherwise it works; for instance 90 degrees is 0.25 and surely enough In situations not involving e in relation to angular representations via Euler, f cannot replace e.I'm all for having parallel trig functions in libraries that work with turns, though.
The annoying 2π factor shows up in lots of places though. Should way, say, in electronics, redefine a new version of capacitive reactance which doesn't have 2πf in the denominator, but only f?