[Python-ideas] Fwd: Trigonometry in degrees
Stephan Houben
stephanh42 at gmail.com
Mon Jun 11 14:04:31 EDT 2018
2018-06-11 19:33 GMT+02:00 Michael Selik <mike at selik.org>:
> Whoops, it turns out Euler's formula does work! I expected imprecision,
> but at least one test matched.
>
> x = 42
> cos(x) + 1j * sin(x) == e ** (1j * x)
>
I think you will find it holds for any x (except inf, -inf and nan).
The boat is less leaky than you think; IEEE floating-point arithmetic goes
out of its way to produce exact answers whenever possible.
(To great consternation of hardware designers who felt that
requiring 1.0*x == x was too expensive.)
> I suppose that's because it's radians.
>
Well, the formula obviously only holds in exact arithmetic
if cos and sin are the versions taking radians.
Stephan
>
>
> On Mon, Jun 11, 2018, 10:24 AM Michael Selik <mike at selik.org> wrote:
>
>> Would sind and cosd make Euler's formula work correctly?
>>
>> sind(x) + i * sind(x) == math.e ** (i * x)
>>
>> I suspect that adding these functions is kind of like those cartoons
>> where the boat is springing leaks and the character tried to plug them with
>> their fingers. Floating point is a leaky abstraction.
>>
>> Perhaps you'd prefer an enhancement to the fractions module that provides
>> real (not float) math?
>>
>
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