Re: 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
>>
>>
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>

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