Re: [math-fun] Does this define sin(z)?

Sin(x) = x + O(x^3), Cos(x) = 1 - (1/2)*x^2 + O(x^4); Along with angle doubling rules: http://mathworld.wolfram.com/Double-AngleFormulas.html Does this define Sin(x) and Cos(x)??? —Brad

On Dec 13, 2019, at 8:06 AM, Bill Gosper <billgosper@gmail.com> wrote:

1) sin(0) := 0 and

2) |sin(x) - sin(y)| ≤ |x - y| and

3) sin(x) = sin(x/3) (3 - 4 sin(x/3)^2).

Note that 2) isn't even true, e.g. x=0, y=i. If this means "No", then what about for real z? —rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun