Question 1205297


{{{sin^2(x)-(1/2)sin(x)-1/2=0}}}....both sides multiply by {{{2}}}


{{{2sin^2(x)-sin(x)-1=0}}}...replace {{{sin(x)}}} with {{{u}}}

{{{2u^2-u-1=0}}}...factor

{{{(2 u + 1) (u - 1)=0}}}


solutions:

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

replace {{{u}}} with {{{sin(x)}}}

{{{sin(x)=-1/2}}}
{{{sin(x)=1}}}


{{{x=sin^-1(-1/2)}}} =>{{{x=-pi/6}}}

{{{x=sin^-1(1) }}}=>{{{x=pi/2}}}


solutions in given interval {{{0 <= x <= 2pi}}}:

{{{x = pi/2}}} =>{{{x=90}}}° 

{{{x = (7pi)/6}}} =>{{{x=210}}}° 

{{{x = (11pi)/6 }}}=>{{{x=330}}}°