/int/ Mathematical

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>>75158555

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>>75158555
Thank me later on your tesis footnotes, Ivan

>>75162414
>ili
i didnt know there was russians in urgay

I would just do this I guess

https://en.m.wikipedia.org/wiki/Newton%27s_method

>>75162442
we are a multicultural country

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R8 my work

>>75158555
do your homework by yourself mikhali

>>75158555
>math
Plebs

>>75162735
>disliking math
brainlet

>>75162810
Not that I dislike it. I dislike doing it, now I just write it up in python and solve it numerically using the 4th order Runge-Kutta method so I don't have to do it anymore

>>75158555
cos(3π/2-x) can be written as -sin(x) by using simple properties of sine and cosine

cos(2x) is equal to 1-2(sin(x))^2

thus you can write you equation as (write sin(x) as y for simplicity)
2(1-2y^2) - 4y z + 1 = 0
from which you get
(1-2y)(3+2y)=0

thus y=1/2 or y=3/2
rewritting that

sin(x)=1/2 or sin(x)=3/2

Because |sin(x)|<=1 you discard the 3/2 solution

sin(x) = 1/2 happens only when x=π/6 + some multiple of 2π

x=π/6 + some multiple of 2π are all the solution of your equation.

>>75163312
oh wait
sin(x)=1/2 can happen at π/6 as well as π-π/6 which is 5π/6

Therefore all the solutions are

π/6 + n(2π)
5π/6 + n(2π)

where n is an integer

>>75158555
>radians
REEEEEEEEEEEEEEEEEEEEEEEEEE

>>75162604
nice

>>75163502
P L E B
L
E
B

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Ok this is a fun one. There is device that has air trapped inside it as water flows through in a streamline manner, V0 is the rate at which water goes in and V1 is the rate at which it goes out. Modeling h2 as a damped harmonic oscillator, give the differential equation that represents the volume that goes out as a function of the volume that goes in.

mathematician reporting in

plug it into your numerical solver of choice