Comment Re:Wow (Score 1) 966
This will not break into the calculus I think. The reason that sin and cosine are so big in calculus has little to do at all with their relation to angles and lengths, it has to do with these relations:
d^2/(dx)^2 f(x) = -f(x)
e(jx) = cos(x) + j*sin(x)
(Yes, I know, those equations are related)
These quadrances and spreads won't scale that way. For an acute angle, the spread is equal to the square of the sin. Obviously, the solution to the simple harmonic equation is going to be rather difficult to express in terms of spread rather than phase! I think the cos and sin's place in calculus is pretty safe.
d^2/(dx)^2 f(x) = -f(x)
e(jx) = cos(x) + j*sin(x)
(Yes, I know, those equations are related)
These quadrances and spreads won't scale that way. For an acute angle, the spread is equal to the square of the sin. Obviously, the solution to the simple harmonic equation is going to be rather difficult to express in terms of spread rather than phase! I think the cos and sin's place in calculus is pretty safe.
