Question 1136559


{{{sin (2t )+ sin( t) = 0}}} , in the interval [{{{0}}}, {{{2pi}}})


Use the following identity : {{{sin (2t)=2 cos(t)sin(t)}}}


{{{2cos(t)sin(t)+ sin( t) = 0}}}........factor out {{{ sin( t)}}}


{{{sin( t)(2cos(t) + 1) = 0}}}


Solving each part separately:


{{{sin( t) = 0}}}  => in the interval [{{{0}}}, {{{2pi}}}) for  {{{t=0}}}, {{{t= pi}}} , {{{t=2pi}}}
 
or

{{{(2cos(t) + 1) = 0}}}=> in the interval [{{{0}}}, {{{2pi}}})  for  {{{t=2pi/3}}},  {{{ t=4pi/3}}}



Combine all the solutions:

 {{{t=0}}}, {{{t= pi}}} , {{{t=2pi}}}, {{{t=2pi/3}}},  {{{ t=4pi/3}}}