Question 1180791


Solve each of the following for {{{0 <= theta <= 360 }}}°

{{{3sin^2 (theta) + 2sin( theta) = 0}}}

{{{(3sin(theta) + 2)sin( theta) = 0}}}

solutions:

if {{{(3sin(theta) + 2) = 0}}}=>{{{3sin(theta)=- 2}}}=>{{{sin(theta)=- 2/3}}}
{{{sin^-1(-2/3)=-0.72972}}}

since given {{{0 <= theta <= 360 }}}°
{{{theta=180+sin^-1(- 2/3)}}}° 
{{{theta=360-sin^-1(- 2/3)}}}° 

then  
{{{theta=180-0.72972}}}
{{{theta=180-41.81}}}° 
{{{theta=138.19}}}° 

{{{theta=360-(-41.81)}}}° 
{{{theta=360+41.81}}}° 
{{{theta=41.81}}}° 

if {{{sin(theta) = 0}}}

{{{theta=sin^-1(0)}}}
{{{theta=0}}}°
{{{theta=0+180}}}°
{{{theta=180}}}°
{{{theta=0+360}}}°
{{{theta=360}}}°

combine solutions:

{{{sin(theta) = 0}}}
{{{theta=41.81}}}° 
{{{theta=138.19}}}° 
{{{theta=180}}}°
{{{theta=360}}}°