Re: 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
>>>
>>>

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