Re: standard trig functions for degrees ?

Just converting back and forth between *sin *and *sind* is easy enough.
There are various ways to do it. Probably the cleanest is to use the
pattern-matching facility.
You should be able to do it ... and then maybe share it with the community
as a *share* package.

But I would strongly oppose adding that to the core system.

Maxima is a symbolic system, and functions in the core system should
support basic symbolic operations like differentiation, expanding as
series, various simplifications, etc., not just numeric evaluation....
(Although I'm sure there are counterexamples where we don't live up to that
ideal.)

Another problem is that Maxima generally likes to have a quasi-canonical
representation for each concept. We don't have both *exp(x)* and *%e^x*,
for example. It's true that we have both *gamma(x) *and *(x-1)!* -- which
does add complications. I sometimes wonder why we didn't standardize on one
or the other and select the output form with a switch. (Yes, that wouldn't
be entirely trivial...).

           -s



On Tue, Apr 28, 2026 at 10:20 AM Henry Baker <[email protected]> wrote:

> Hi Stavros:
>
>
>
> You're way ahead of me.
>
>
>
> I wasn't thinking of anything like a "units" package, with units like
> "degrees" or "radians".  While that might be nice, it's far more ambitious
> than I had in mind.
>
>
>
> I was thinking more along the lines of "exponentialize" which converts
> trig functions into exponentials (and the reverse).
>
>
>
>
>
> -----Original Message-----
> From: Stavros Macrakis <[email protected]>
> Sent: Apr 27, 2026 3:45 PM
> To: <[email protected]>
> Cc: <[email protected]>, Robert Dodier <
> [email protected]>
> Subject: Re: [Maxima-discuss] standard trig functions for degrees ?
>
>
> Take a look at the examples I sent before, where that approach doesn't
> work. For convenience, I'm repeating them below:
>
> If you're working in degrees, *limit(sind(x)/x,x,0)* gives *%pi/180*; is
> that what is expected, or does the user want to see *(%pi/180)°* or maybe
> *1*? Note that *sin/cos/etc. *don't appear in the result.
>
> How do you write the Taylor expansion of sind(x)? The straightforward way
> gives
>
>
> taylor(sind(x),x,0,3) =>
>              (%pi*x)/180-(%pi^3*x^3)/34992000
>
>
> Note that *sin/cos/etc. *don't appear in the result. Do you write that as
> something like
>
>
> (x*°*) -(x*°*)^3/6
>
>
> How do you know to do that?
>
> On Mon, Apr 27, 2026 at 6:33 PM Henry Baker <[email protected]> wrote:
>
>> No, simply given an expression with "sin" or "asin", rewrite each
>> occurrence with the "sind" or "asind" with the appropriate fudge factor
>> (%pi/180 or 180/%pi) stuck in; ditto in reverse.  Then resimplify, of
>> course.
>>
>>
>>
>>
>>
>> -----Original Message-----
>> From: Stavros Macrakis <[email protected]>
>> Sent: Apr 27, 2026 3:24 PM
>> To: <[email protected]>
>> Cc: <[email protected]>, Robert Dodier <
>> [email protected]>
>> Subject: Re: [Maxima-discuss] standard trig functions for degrees ?
>>
>>
>> I'm not sure what you're proposing -- that every function that takes trig
>> functions as input or output will have to be modified?
>>
>> On Mon, Apr 27, 2026 at 6:20 PM Henry Baker <[email protected]> wrote:
>>
>>> Well, as ugly as switches are, I suppose one could switch from
>>> primitives sind/cosd/tand/asind/acosd/atand to primitives
>>> sin/cos/tan/asin/acos/atan or back again with a switch.
>>>
>>>
>>>
>>> I agree that things get ugly when using degrees instead of radians, but
>>> some usages of degrees are embedded so tightly into the application context
>>> that it seems perverse to insist on radians.
>>>
>>>
>>>
>>> Also, if we are sufficiently knowledgeable about the number %pi/180 --
>>> e.g., identities about its various powers -- some "nice" things may happen
>>> that are a bit less obvious when working with radians.
>>>
>>>
>>>
>>>
>>>
>>> -----Original Message-----
>>> From: Stavros Macrakis <[email protected]>
>>> Sent: Apr 27, 2026 3:09 PM
>>> To: Henry Baker <[email protected]>
>>> Cc: <[email protected]>, Robert Dodier <
>>> [email protected]>
>>> Subject: Re: [Maxima-discuss] standard trig functions for degrees ?
>>>
>>>
>>> Henry,
>>>
>>> I really don't know much about working in degrees. Like Ray, the last
>>> time I did that was in high school.
>>>
>>> If you're working in degrees, how do you write, say, the Taylor
>>> expansion of sind(x)? The straightforward way gives
>>>
>>>
>>> taylor(sind(x),x,0,3) =>
>>>              (%pi*x)/180-(%pi^3*x^3)/34992000
>>>
>>>
>>> Do you write that as something like
>>>
>>>
>>> (x*°*) -(x*°*)^3/6
>>>
>>> ?
>>>
>>> On Mon, Apr 27, 2026 at 5:15 PM Stavros Macrakis <[email protected]>
>>> wrote:
>>>
>>>> I don't know what exactly Henry wants. If it's just numeric
>>>> computation, that's trivial. As he says, it's < 1k of code, which he can
>>>> write himself.
>>>>
>>>> The hard part is symbolic computation.
>>>>
>>>> I'd think that someone working in degrees would like to see things like:
>>>>
>>>>
>>>> *sind(x/2),halfangles => sqrt(1-cosd(x))/sqrt(2) *(for 0<x<360)
>>>>
>>>>
>>>> This gets messier. Yes, you can write pattern matching rules that
>>>> change all instances of *cos(...)* to *cosd(...)*, etc.
>>>>
>>>> But what about, say, *limit(sind(x)/x,x,0)*? That gives *%pi/180*; is
>>>> that what is expected, or does the user want to see *(%pi/180)°* or
>>>> maybe *1*? I've never worked in degrees beyond elementary trig, so I
>>>> don't know what the user expects, and whether the system (as opposed to the
>>>> user) needs to keep track of degrees vs. radians.
>>>>
>>>> Or am I overthinking it?
>>>>
>>>>           -s
>>>>
>>>> On Mon, Apr 27, 2026 at 4:45 PM Robert Dodier <[email protected]>
>>>> wrote:
>>>>
>>>>> On Mon, Apr 27, 2026 at 12:48 PM Henry Baker <[email protected]>
>>>>> wrote:
>>>>>
>>>>> > A number of computer languages -- e.g., Fortran -- support trig
>>>>> functions over degrees -- e.g., sind(x), cosd(x), tand(x), asind(x), etc.
>>>>> >
>>>>> > I know it's "trivial", but could Maxima please go ahead a define
>>>>> standardly the trig functions over degrees?  We're talking about about
>>>>> increasing the core system at most by perhaps 1K bytes !
>>>>>
>>>>> Well, maybe the code is trivial, but the increased mental burden is
>>>>> not ... Instead of creating new functions, I am OK with two functions,
>>>>> radians(x) to get radians from degrees and degrees(x) to get degrees
>>>>> from radians. Then one can call those whenever it makes sense.
>>>>>
>>>>> We could make those simplifying functions. Just thinking out loud here.
>>>>>
>>>>> Hmm, maybe degrees(x) should represent x degrees, like radians(x)
>>>>> represents x radians. radians(x) simplifies to x and degrees(x)
>>>>> simplifies to x*%pi/180. E.g. sin(degrees(90)) --> sin(%pi/2), etc.
>>>>>
>>>>> I think I'm leaning towards degrees(x) representing x degrees. What
>>>>> does anyone else think?
>>>>>
>>>>> Robert
>>>>>
>>>>>
>>>>> _______________________________________________
>>>>> Maxima-discuss mailing list
>>>>> [email protected]
>>>>> https://lists.sourceforge.net/lists/listinfo/maxima-discuss
>>>>
>>>>

_______________________________________________
Maxima-discuss mailing list
[email protected]
https://lists.sourceforge.net/lists/listinfo/maxima-discuss