POV-Ray : Newsgroups : povray.advanced-users : Stumped by desk lamp trig equation : Re: Stumped by desk lamp trig equation Server Time28 Jan 2023 15:07:29 EST (-0500)
 Re: Stumped by desk lamp trig equation
 From: Cousin Ricky Date: 7 Aug 2022 13:54:08 Message: <62effc40\$1@news.povray.org>
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On 2022-08-07 10:59 (-4), kurtz le pirate wrote:
> On 06/08/2022 23:57, Cousin Ricky wrote:
>
>> Does this imply that I would need to program a numeric solution into my
>> macro?
>
> I am afraid that it is not possible to solve literally an equation which
> makes appear at the same time t, sin(t) and cos(t). A bit like in
> differential equations with x and dx.

Then numerical computation it will have to be, albeit in SDL.

> Literal solutions never exist (except for school cases).

I suspected those examples in high school were conveniently contrived.

> Another trail.
> Let sin(x) = T and cos(x) = U, the equation becomes :
> (g - c/x)T + hU - a = 0
>
> Wolfram proposes a more "usable" result.
> <https://www.wolframalpha.com/input?i=solve+%28g+-+c%2Fx%29T+%2B+hU+-+a+%3D+0>
>
> x = cT/(-a+gT+hU) with a!=gt+hU & cT!=0
>
>
> Maybe more adapted to your needs ?

I'll take a look at it.  Thanks!
```