/sci/ - Science & Math

>>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.

>>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

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

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

>>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.

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

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

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

r = a + d*cos(theta)

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