[Python-ideas] Trigonometry in degrees

[Ryan Gonzalez]

You could always do e.g. math.sin(math.degress(radians)) and so forth...


On June 7, 2018 3:07:21 PM Robert Vanden Eynde 
<robertvandeneynde at hotmail.com> wrote:

> I suggest adding degrees version of the trigonometric functions in the math 
> module.
>
> - Useful in Teaching and replacing calculators by python, importing 
> something is seen by the young students much more easy than to define a 
> function.
>
> - Special values could be treated, aka when the angle is a multiple of 90, 
> young students are often surprise to see that cos(pi/2) != 0
>
> Testing for a special value Isn't very costly (x % 90 == 0) but it could be 
> pointed out that there is a small overhead using the "degrees" equivalent 
> of trig function because of the radians to degrees conversion And the 
> special values testing.
>
> - Standard names will be chosen so that everyone will use the same name 
> convention. I suggest adding a "d" like sind, cosd, tand, acosd, asind, 
> atand, atan2d.
>
> Another option would be to add "deg" or prepend "d" or "deg" however the 
> name should be short.
>
> sind, dsin, sindeg or degsin ?
>
> We can look in other languages what they chose.
>
> Creating a new package like 'from math.degrees import cos' however I would 
> not recommend that because "cos" in the source code would mean to lookup 
> the import to know if it's in degrees or radians (and that leads to very 
> filthy bugs). Also "degrees" is already so the name would have to change 
> the name of the package.
>
> - Also in the cmath module. Even though the radians make more sense in the 
> complex plane. The same functions sin cos tan, asin acos atan, alongside 
> with phase and polar.
>
> Here's my current implementation :
>
> def cosd(x):
>     if x % 90 == 0:
>         return (1, 0, -1, 0)[int(x // 90) % 4]
>     else:
>         return cos(radians(x))
>
> def sind(x):
>     if x % 90 == 0:
>         return (0, 1, 0, -1)[int(x // 90) % 4]
>     else:
>         return sin(radians(x))
>
> def tand(x):
>     if x % 90 == 0:
>         return (0, float('inf'), 0, float('-inf'))[int(x // 90) % 4]
>     else:
>         return tan(radians(x))
>
> The infinity being positive of negative is debatable however, here I've 
> chosen the convention lim tan(x) as x approaches ±90° from 0
>
> def acosd(x):
>     if x == 1: return 0
>     if x == 0: return 90
>     if x == -1: return 180
>     return degrees(acos(x))
>
> def asind(x):
>     if x == 1: return 90
>     if x == 0: return 0
>     if x == -1: return -90
>     return degrees(asin(x))
>
> However, currently [degrees(acos(x)) for x in (1,0,-1)] == [0, 90, 180] on 
> my machine so maybe the test isn't necessary.
>
> Testing for Special values of abs(x) == 0.5 could be an idea but I don't 
> think the overhead is worth the effort.
>
> Probably this has already been discussed but I don't know how to check that.
>
>
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