/sci/ - Science & Math » Thread #11152532

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Math Challenge

Anonymous Sat 16 Nov 20:51:08 2019 No.11152532 View Reply Original Report

Quoted By: >>11152556 >>11152573 >>11152629

I haven't figured it out yet, but do you think it is possible to express d as a simple function of r,a and theta ?

Assuming r > 0 and 0 < a < r and 0 < theta < pi

Anonymous

Anonymous Sat 16 Nov 2019 21:04:39 No.11152556 Report

Quoted By: >>11154237

>>11152532
r^2 = a^2 + d^2 - 2 a d cos(180° - theta)
Known as the law of cosines.
You can simply use the quadratic formula to solve this for d.

Anonymous

Anonymous Sat 16 Nov 2019 21:10:44 No.11152573 Report

Quoted By: >>11152587 >>11152626

>>11152532
i don't think you'd need theta, if a = 0 then d = r, d decreases by a certain rate as a increases, all you need to know is a and r

Anonymous

Anonymous Sat 16 Nov 2019 21:13:18 No.11152587 Report

Quoted By:

>>11152573
or you could express it with theta and without a

Anonymous

Anonymous Sat 16 Nov 2019 21:14:56 No.11152595 Report

Quoted By:

Oh, i forgot to mention that a and r are contant, only theta can change

Anonymous

Anonymous Sat 16 Nov 2019 21:23:46 No.11152626 Report

Quoted By:

>>11152573
The solution is only unique for a = 0. For the same a and r, you can draw any number of d's ranging from r-a to r+a so long as a !=0. Just try it.

Anonymous

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Anonymous Sat 16 Nov 2019 21:24:24 No.11152629 Report

Quoted By:

>>11152532
See >>11152621
And use /sqt/ next time.

Anonymous

Anonymous Sat 16 Nov 2019 21:35:48 No.11152664 Report

Quoted By:

I tried to apply the law of cosines and after solving the quadratic equation, I get:

d = a*sin(theta) - sqrt(r2-a2*cos2(theta))

but it doesn't seem to fit for theta = 0 : my formula gives d = sqrt(r2-a2) whereas I should find r-a

Anonymous

Anonymous Sat 16 Nov 2019 22:09:49 No.11152757 Report

Quoted By:

Ok I finally found the right after : there were mistakes in my formula.

So, the result is :

for a and r fixed,
d(theta) = sqrt(r^2-a^2*sin^2(theta)) - a*cos(theta)

Works for theta = 0 and theta = pi.

Thanks guys for help

Anonymous

Anonymous Sun 17 Nov 2019 08:18:16 No.11154192 Report

Quoted By:

r = a + d*cos(theta)

Anonymous

Anonymous Sun 17 Nov 2019 08:41:26 No.11154237 Report

Quoted By:

>>11152556
>He answered the question and so the thread should have been over, but retarded faggots still wanted to put in their two cents.

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