# [Python-ideas] Trigonometry in degrees

Rob Speer rspeer at luminoso.com
Thu Jun 7 16:45:42 EDT 2018

```You meant math.radians(degrees), and Robert already mentioned the problem
with this:

6.123233995736766e-17

On Thu, 7 Jun 2018 at 16:22 Ryan Gonzalez <rymg19 at gmail.com> wrote:

> 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:
>>
>> def sind(x):
>>     if x % 90 == 0:
>>         return (0, 1, 0, -1)[int(x // 90) % 4]
>>     else:
>>
>> def tand(x):
>>     if x % 90 == 0:
>>         return (0, float('inf'), 0, float('-inf'))[int(x // 90) % 4]
>>     else:
>>
>> 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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