Question

3 sin^x + 4 sinx + 1 = 0

Answer 1

$3 sin^2x + 4 sinx + 1 = 0 \ D=16-4*3*1=16-12=4 \ sinx_1= frac{-4+2}{6} = -frac{2}{6} =- frac{1}{3} ~~~~~~~~~~~~~~~~~~sinx_2= frac{-4-2}{6}=- frac{6}{6} =-1 \ sinx=- frac{1}{3} ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~sinx=-1 \ \ x=(-1)^{k+1} arcsinfrac{1}{3} + pi k~~~~~~~~~~~x=- frac{ pi }{2} +2 pi k \ kin Z$