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I have the following formula:
tan(theta) * R1 = sin(theta) * R2
R1 and R2 are known. How do I solve for theta? Thanks!
-Mike
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On Mon, 31 Aug 2009 04:48:08 -0400, SharkD <mik### [at] gmail com> wrote:
>I have the following formula:
>
> tan(theta) * R1 = sin(theta) * R2
>
>R1 and R2 are known. How do I solve for theta? Thanks!
>
>-Mike
It has been a very, very long time since I did anything like this and I could
be far out. So don't take this for gospel ;)
tan(theta) * R1 = sin(theta) * R2
Therefore: tan(theta) = sin(theta) * r2/r1
But tan(theta) = sin(theta) /cos(theta)
Therefore: sin(theta) /cos(theta) = sin(theta) * r2/r1
Divide both sided by sin(theta) /cos(theta)
1 = (sin(theta) * cos(theta) *r2)/(r1 * sin(theta) )
1 = cos(theta) *r2/r1
Therefore: cos(theta) = r2/r1
--
Regards
Stephen
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> 1 = cos(theta) *r2/r1
>
> Therefore: cos(theta) = r2/r1
You messed up at the very last step :-)
Easier if at this step:
sin(theta)/cos(theta) = sin(theta) * r2/r1
You just cancel the sin(theta) term on each side, leaves you with:
1/cos(theta) = r2/r1
Taking the reciprocal of both sides then leaves you with the answer.
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On Mon, 31 Aug 2009 11:57:28 +0200, "scott" <sco### [at] scottcom> wrote:
>
>You messed up at the very last step :-)
LOL I inverted the "r1/r2" when I was checking.
I said it was a long time ago.
But it at least got someone to check it ;)
--
Regards
Stephen
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scott wrote:
> You just cancel the sin(theta) term on each side, leaves you with:
>
> 1/cos(theta) = r2/r1
>
> Taking the reciprocal of both sides then leaves you with the answer.
>
Thank you! I forgot that tan = sin/cos.
-Mike
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Among other things, SharkD saw fit to write:
>> You just cancel the sin(theta) term on each side, leaves you with:
>>
>> 1/cos(theta) = r2/r1
>>
>> Taking the reciprocal of both sides then leaves you with the answer.
>>
>
> Thank you! I forgot that tan = sin/cos.
You all missed the last step:
theta = arccos(R1/R2) ;-)
--
light_source{9+9*x,1}camera{orthographic look_at(1-y)/4angle 30location
9/4-z*4}light_source{-9*z,1}union{box{.9-z.1+x clipped_by{plane{2+y-4*x
0}}}box{z-y-.1.1+z}box{-.1.1+x}box{.1z-.1}pigment{rgb<.8.2,1>}}//Jellby
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SharkD wrote:
> I have the following formula:
>
> tan(theta) * R1 = sin(theta) * R2
>
> R1 and R2 are known. How do I solve for theta? Thanks!
>
theta = 0 ;)
--
mailto:jeb### [at] freefr
http://jeberger.free.fr
Jabber: jeb### [at] jabberfr
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> Easier if at this step:
>
> sin(theta)/cos(theta) = sin(theta) * r2/r1
>
> You just cancel the sin(theta) term on each side, leaves you with:
>
> 1/cos(theta) = r2/r1
However, now that you've divided both sides by sin(theta), you're only
solving the equation over values where sin(theta) is not 0. You have to
check that possibility separately, and it looks like the equation is
trivially true when sin(theta) = 0, or when theta = n*pi. (As well as the
solution you gave.)
- Slime
[ http://www.slimeland.com/ ]
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