POV-Ray : Newsgroups : povray.advanced-users : Stumped by desk lamp trig equation : Re: Stumped by desk lamp trig equation Server Time23 Sep 2023 14:16:01 EDT (-0400)
 Re: Stumped by desk lamp trig equation
 From: kurtz le pirate Date: 7 Aug 2022 10:59:13 Message: <62efd341\$1@news.povray.org>
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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.

Literal solutions never exist (except for school cases).

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

--
Kurtz le pirate
Compagnie de la Banquise
```