POV-Ray : Newsgroups : povray.advanced-users : Stumped by desk lamp trig equation : Re: Stumped by desk lamp trig equation Server Time28 Jan 2023 14:31:46 EST (-0500)
 Re: Stumped by desk lamp trig equation
 From: kurtz le pirate Date: 6 Aug 2022 13:32:06 Message: <62eea596\$1@news.povray.org>
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"dateCreated": "2022-08-06T17:32:06+00:00",
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On 06/08/2022 18:24, Cousin Ricky wrote:
> I want to aim a desk lamp by specifying where it should point.  P(x,y)
> is where to aim the lamp, c is the length of the flexible part of the
> neck, a is an additional rigid distance to the central axis of the lamp
> hood, and f is the angle to bend the neck.  The initial equation was
> huge and ugly, but I managed to simplify it considerably, to this form:
>
>   (x - c/f) * sin(f) + y * cos(f) = a
>
> But now I'm stuck.  Variables a, c, x, and y are given, and I need to
> solve for f.  I plugged it into Wolfram Alpha, but it gave up.  I don't
> even know if a paid subscription would find a solution, and I would
> hardly use the service enough to justify a subscription anyway.  Does
> anyone have an idea of how to proceed with the equation?  Or should I
> gamble that Wolfram Alpha Pro can solve it and pay for one month?
>

To test your equation, I replaced the a, c, x and y by numerical values.
Wolfram solve the equation but only numerically because apparently there
is not only one solution...

<https://www.wolframalpha.com/input?i=solve+++%283+-+4%2Fx%29+*+sin%28x%29+%2B+5+*+cos%28x%29+%3D+2>

Puzzled !

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