/sci/ - Science & Math

[Anonymous No.3235426]

cos (x) + cos (3x) = 1/2
Trying to find solutions for x over 0 < x < pi but I'm fucking clueless
Any help/clues/hints/anything?

[Anonymous No.3235441]

http://www.wolframalpha.com/input/?i=cos+%28x%29+%2B+cos+%283x%29+%3D+1%2F2+from+0+to+pi+faggot

http://www.wolframalpha.com/input/?i=cos+%28x%29+%2B+cos+%283x%29+%3D+1%2F2

sage

[Anonymous No.3235447]

cos (x) + cos (3x) = 1/2
cos^3(x)+cos(x)-3 sin^2(x) cos(x) = 1/2
cos^3(x)+cos(x)-3 sin^2(x) cos(x) = 1/2

replace sin^2(x) with 1-cos^2(x)
set y = cos(x)
now you have a polynomial in y
solve for y
get x
the answer is:


http://www.wolframalpha.com/input/?i=cos%20%28x%29%20%2B%20cos%20%283x%29%20%3D%201%2F2&t=ff3tb0
1

[Anonymous No.3235449]

>>3235441
I got that far. I have the solutions. I just need to know HOW to get them. But cheers.

[Anonymous No.3235467]

>>3235447
'eyyyy! Now we're getting somewhere.
In return, farm animals.