Question 1158674
use the given conditions to find the exact value of the expression: 

{{{sin(a)=(-5/13)}}}, {{{tan(a)> 0}}}, {{{sin(a-(2pi/3))}}}

Since {{{sin(a) = -5/13}}} , and {{{tan (a) > 0 }}}, it follows that {{{cos(a) < 0}}} (Third quadrant)

So 

{{{cos (a) =-sqrt( 1 - (5/13)^2 )}}}

 {{{cos (a) = -sqrt((169 - 25)/169 )}}}

 {{{cos (a)  = - 12/13}}}


so,

{{{sin(a-(2pi/3))=sin(a)*cos(2pi/3)-cos(a)*sin(2pi/3)}}}
 

Substituting values: {{{sin(a)=(-5/13)}}},{{{cos(2pi/3)=-1/2}}}, {{{cos (a)  = - 12/13}}}, {{{sin(2pi/3)=sqrt(3)/2}}}
 

{{{sin(a-(2pi/3))=(-5/13)(-1/2)-(-12/13)(sqrt(3)/2)}}}
 

{{{sin(a-(2pi/3))=(5/26)+12 sqrt(3)/26}}}
 

{{{sin(a-(2pi/3))=(5+12sqrt(3))/26}}}


{{{sin(a-(2pi/3))=5/26 + (6sqrt(3))/13}}}