Question 1203696
 Find all solutions on
[{{{ 0}}}, {{{ 2pi}}}). (Enter your answers as a comma-separated list. Round your answers to four decimal places.)


{{{ 12sin^2(x) + 8sin(x) + 1 = 0}}}....factor

{{{ 12sin^2(x) +2sin(x) + 6sin(x)+ 1=0}}}

{{{ (12sin^2(x) +2sin(x)) + (6sin(x)+ 1)=0}}}

2{{{ sin(x)(6sin(x) +1) + (6sin(x)+ 1)=0}}}

{{{ (2sin(x) + 1) (6sin(x) + 1)=0}}}


solutions:


{{{ 2sin(x) + 1=0}}} => {{{sin(x) =-1/2}}}

{{{ x = (1/6) (12pi* n + pi)}}}, {{{ n}}} element{{{  Z}}}

{{{ x = (1/6) (12pi* n - pi)}}},{{{  n }}}element{{{  Z}}}

or

{{{ 6sin(x) + 1=0}}}=> {{{sin(x) =-1/6}}}

{{{ x = 2 pi* n +sin^(-1)(1/6)}}}, {{{ n }}}element {{{ Z}}}

{{{ x = 2 pi* n - sin^(-1)(1/6)}}}, {{{ n}}} element {{{ Z}}}



 solutions on [{{{ 0}}},{{{  2pi}}}):


{{{ x  =  pi +sin^(-1)(1/6)}}}  or {{{x=pi+0.16744}}}

{{{ x = - sin^(-1)(1/6) }}} or {{{x=-0.16744+2pi}}}

{{{ x=7pi/6}}}

{{{ x=11pi/6}}}


Round your answers to four decimal places

{{{ x =  3.3090 }}} 
{{{ x = 6.1157}}}
{{{ x=3.6652}}}
{{{ x=5.7596}}}


{{{x}}}={ {{{ 3.3090}}},{{{3.6652}}},{{{5.7596}}},{{{6.1157}}} }