Math Is Fun Forum

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Finding sin(10)

From the triple angle formula for sin, using sin(30) i get sin(10) as being the solution to a cubic equation:
in solving this cubic using cardano's method i get a complex number, who's real part is sin(10)
in solving again using cardano's but taking the opposite sign when solving the quadratic, i get an imaginary number who's value is the negative of the previous complex number's imaginary part, which means that in the end: i have this as a formula for sin(10)

it's quite ugly, anyone have any ideas on getting a much much nicer one? LOL

Last edited by luca-deltodesco (2008-11-30 06:39:52)

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Kurre

Member

Registered: 2006-07-18

Posts: 280

Re: Finding sin(10)

Tbh, that formula does not seem to be any progress at all, since

Which after simplifying is just sin(pi/18).