Re: high school trigonometry?
- From: ram <ram@xxxxxxxxxxxxxxxx>
- Date: Mon, 18 Dec 2006 14:01:13 GMT
Solid State 80 wrote:
Dray the joints and do the math -- nothing more that simple analytic trigonometry is required.
I did just that. And from your Google advice and the other responder's other links I have some promising leads and more geometry/trigonometry challenges.
But there remains the matter of the formula my methods came up with, and the fact that it gives good answers, modulo a supplementary angle here and there.
In developing the miter angle, for example, I had an intermediate expression
Cos[Theta]^2 / Sin[Phi]^2 + Sin[Theta]^2 - 1
which yielded nicely to the use of cos^2 x + sin^2 x = 1, giving me
Cos[Theta]^2 / Tan[Phi]^2
Hence my belief that my expression for the bevel angle could also be, er, improved.
Leave the carpentry out of it! Since the expression
ArcCos[ Cos[Theta]^2 Sin[Phi] + Sin[Theta]^2 ]
seems to work like
bladeTilt = ArcSin[Sin[B] Sin[A/2]]
I think the uglier expression could be simplified using other trigonometric manipulations.
How can I get from something like
Cos[Theta]^2 Sin[Phi] + Sin[Theta]^2
to
Sin[B] Sin[A/2]
Where Theta has a simple relation to B and Phi is simply related to A?
Meanwhile I will try again from first principles other approaches to the derivation of the simple formula on all the carpentry websites.
--
rob
.
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- From: ram
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- From: Solid State 80
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