Question 1159666

Use the given conditions to find the exact value of the expression.
{{{sin (alpha) = -5/13}}} 
{{{tan (alpha) > 0 }}}
{{{sin (alpha - 5pi/3)}}}


{{{cos(alpha)=-sqrt(1-sin^2(alpha) )}}}

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

{{{cos(alpha)=-sqrt(1-25/169 )}}}

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

{{{cos(alpha)=-sqrt(144/169 )}}}

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


{{{tan (alpha) = (-5/13 )/(-12/13) }}}

{{{ tan (alpha) = 5/12}}}=>{{{tan (alpha) > 0 }}}



{{{sin (alpha - 5pi/3)}}}->use


{{{sin (alpha - beta)=sin(alpha) cos(beta) - cos(alpha)sin(beta) }}}


let {{{beta=5pi/3}}}, already given {{{sin (alpha) = -5/13 }}}, and {{{cos(alpha)=-12/13}}}


{{{sin (alpha - 5pi/3)=-(5/13)cos(5pi/3) - (-12/13) sin(5pi/3)}}}....{{{cos(5pi/3)=1/2}}}, {{{sin(5pi/3)=-sqrt(3)/2}}}


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

{{{sin (alpha - 5pi/3)=-5/26 -(6sqrt(3))/13}}}

{{{sin (alpha - 5pi/3)=-5/26 -(6sqrt(3))/13}}}