| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
We have had several discussions here on this problem concerning the
relationship of angle c and b. Any ideas??? -art-
Given a right triangle, a, b, e^a, with c being the angle opposite b.
What are the values of a and b in real numbers, when b equals the magnitude
of c (measured in radians.)
added info:
e^a cos(b)=a
e^a sin(b)=b
ln((a^2 + b^2)^1/2)=a
arctan(b/a)=b
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e^a / |
/ |b
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/ c |
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a
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 1630.1 | i dont understand your diagram | STAR::ABBASI | i^(-i) = SQRT(exp(PI)) | Thu Jun 18 1992 05:17 | 25 |
/|
/ |
e^a / |
/ |b
/ |
/ c |
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a
iam missing something,
why e^a ??
let c= 1 (radian)
then e^2a sin(1)= a
i.e. .8414 e^2a = a
true for all a, then let a=1
then e^2= 1.18
i.e. e= 1.090135 ???
/nasser
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| 1630.2 | e^1 = 2.718281828 | CSC32::COLTER | Thu Jun 18 1992 07:18 | 4 | |
e^1 = 2.718281828
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| 1630.3 | BEING::EDP | Always mount a scratch monkey. | Thu Jun 18 1992 09:23 | 19 | |
Re .0:
I think I understand what you are asking, but your phrasing is not
quite clear, so let me restate the problem to be sure. Let's label the
triangle XYZ, where segment XZ is the hypoteneuse and angle XYZ is the
right angle.
Now the length of segment XY is a, the length of segment XZ is e^a, and
the length of segment YZ is b, correct? And the measure of angle YXZ
in radians is also b? These match the equations you have given.
Observe that from arctan(b/a)=b, we can write a = b/tan(b). Then we
can substitute that into e^a cos(b) = a to get an expression containing
only b. Plotting that expression shows it has a solution at b=pi/2 and
no other solutions between 0 and pi. Pi/2 cannot be a solution because
that makes a right angle. So there are no solutions to your problem.
-- edp
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| 1630.4 | e^(b/tan b)*sin b - b = 0 should do it! | CSC32::COLTER | Mon Jun 29 1992 06:54 | 9 | |
You are correct when you state the key to the problem is a=b/tan b.
Using that information, we obtain the following formula:
e^(b/tan b)*sin b - b = 0.
From this point we plug the equation into a computer and vary b until
we obtain something near 0.
The answer for b is 1.3xxxxxx the proof is left to the reader.
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