[Python-ideas] Trigonometry in degrees

Sat Jun 9 02:18:16 EDT 2018

Indeed what we need for exact math for multiple of 90 (and 30) is ideas from the symbolic libraries (sympy, sage).

Of course the symbolic lib can do more like :

sage: k = var('k', domain='integer')
sage: cos(1 + 2*k*pi)
cos(1)
sage: cos(k*pi)
cos(pi*k)
sage: cos(pi/3 + 2*k*pi)
1/2

But that would concern symbolic lib only I think.

For the naming convention, scipy using sindg (therefore Nor sind nor sindeg) will make the sind choice less obvious. However if Matlab and Julia chooses sind that's a good path to go, Matlab is pretty popular, as other pointed out, with Universities giving "free" licences and stuff. With that regards, scipy wanting to "be a replacement to Matlab in python and open source" it's interesting they chose sindg and not the Matlab name sind.

For the "d" as suffix that would mean "d" as "double" like in opengl. Well, let's remember that in Python there's only One floating type, that's a double, and it's called float... So python programmers will not think "sind means it uses a python float and not a python float32 that C99 sinf would". Python programmers would be like "sin takes float in radians, sind takes float in degrees or int, because int can be converted to float when there's no overflow".

Le sam. 9 juin 2018 à 04:09, Wes Turner <wes.turner at gmail.com<mailto:wes.turner at gmail.com>> a écrit :
# Python, NumPy, SymPy, mpmath, sage trigonometric functions
https://en.wikipedia.org/wiki/Trigonometric_functions

## Python math module
https://docs.python.org/3/library/math.html#trigonometric-functions
- degrees(radians): Float degrees
- radians(degrees): Float degrees

## NumPy
https://docs.scipy.org/doc/numpy/reference/routines.math.html#trigonometric-functions
- degrees(radians) : List[float] degrees
- rad2deg(radians): List[float] degrees
- radians(degrees) : List[float] radians
- deg2rad(degrees): List[float] radians

https://docs.scipy.org/doc/numpy/reference/generated/numpy.sin.html

## SymPy
http://docs.sympy.org/latest/modules/functions/elementary.html#sympy-functions-elementary-trigonometric
http://docs.sympy.org/latest/modules/functions/elementary.html#trionometric-functions

- sympy.mpmath.degrees(radians): Float degrees
- sympy.mpmath.radians(degrees): Float radians

- https://stackoverflow.com/questions/31072815/cosd-and-sind-with-sympy
  - cosd, sind
  - https://stackoverflow.com/questions/31072815/cosd-and-sind-with-sympy#comment50176770_31072815

    > Let x, theta, phi, etc. be Symbols representing quantities in radians. Keep a list of these symbols: angles = [x, theta, phi]. Then, at the very end, use y.subs([(angle, angle*pi/180) for angle in angles]) to change the meaning of the symbols to degrees"

## mpmath
http://mpmath.org/doc/current/functions/trigonometric.html
- sympy.mpmath.degrees(radians): Float degrees
- sympy.mpmath.radians(degrees): Float radians

## Sage
https://doc.sagemath.org/html/en/reference/functions/sage/functions/trig.html

On Friday, June 8, 2018, Robert Vanden Eynde <robertvandeneynde at hotmail.com<mailto:robertvandeneynde at hotmail.com>> wrote:
- Thanks for pointing out a language (Julia) that already had a name convention. Interestingly they don't have a atan2d function. Choosing the same convention as another language is a big plus.

- Adding trig function using floats between 0 and 1 is nice, currently one needs to do sin(tau * t) which is not so bad (from math import tau, tau sounds like turn).

- Julia has sinpi for sin(pi*x), one could have sintau(x) for sin(tau*x) or sinturn(x).

Grads are in the idea of turns but with more problems, as you guys said, grads are used by noone, but turns are more useful. sin(tau * t) For The Win.

- Even though people mentionned 1/6 not being exact, so that advantage over radians isn't that obvious ?

from math import sin, tau
from fractions import Fraction
sin(Fraction(1,6) * tau)
sindeg(Fraction(1,6) * 360)

These already work today by the way.

- As you guys pointed out, using radians implies knowing a little bit about floating point arithmetic and its limitations. Integer are more simple and less error prone. Of course it's useful to know about floats but in many case it's not necessary to learn about it right away, young students just want their player in the game move in a straight line when angle = 90.

- sin(pi/2) == 1 but cos(pi/2) != 0 and sin(3*pi/2) != 1 so sin(pi/2) is kind of an exception.

Le ven. 8 juin 2018 à 09:11, Steven D'Aprano <steve at pearwood.info<mailto:steve at pearwood.info>> a écrit :
On Fri, Jun 08, 2018 at 03:55:34PM +1000, Chris Angelico wrote:
> On Fri, Jun 8, 2018 at 3:45 PM, Steven D'Aprano <steve at pearwood.info<mailto:steve at pearwood.info>> wrote:
> > Although personally I prefer the look of d as a prefix:
> >
> > dsin, dcos, dtan
> >
> > That's more obviously pronounced "d(egrees) sin" etc rather than "sined"
> > "tanned" etc.
>
> Having it as a suffix does have one advantage. The math module would
> need a hyperbolic sine function which accepts an argument in; and
> then, like Charles Napier [1], Python would finally be able to say "I
> have sindh".

Ha ha, nice pun, but no, the hyperbolic trig functions never take
arguments in degrees. Or radians for that matter. They are "hyperbolic
angles", which some electrical engineering text books refer to as
"hyperbolic radians", but all the maths text books I've seen don't call
them anything other than a real number. (Or sometimes a complex number.)

But for what it's worth, there is a correspondence of a sort between the
hyperbolic angle and circular angles. The circular angle going between 0
to 45° corresponds to the hyperbolic angle going from 0 to infinity.

https://en.wikipedia.org/wiki/Hyperbolic_angle

https://en.wikipedia.org/wiki/Hyperbolic_function

> [1] Apocryphally, alas.

Don't ruin a good story with facts ;-)

--
Steve
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