Question 1176583

Find{{{ cos(s + t) }}}


given that 


{{{sin( s) = - sqrt(3)/3}}}, with {{{s}}} in quadrant IV

and {{{sin (t)= -sqrt( 5)/6}}} with {{{t}}} in quadrant IV


if {{{sin( s) = - sqrt(3)/3}}}-> {{{opp/hyp = - sqrt(3)/3}}}


{{{opp=- sqrt(3)}}}
{{{hyp=3}}}

then

{{{adj=sqrt(3^2-(- sqrt(3))^2)}}}

{{{adj=sqrt(9-3)}}}

{{{adj=sqrt(6)}}}


then {{{cos(s)=sqrt(6)/3=sqrt(2/3)}}} -> with {{{s}}} in quadrant IV, {{{cos(s)}}} is > {{{0}}}


if {{{sin (t)= -sqrt( 5)/6}}}-> {{{opp/hyp = - sqrt(5)/6}}}

{{{opp=- sqrt(5)}}}
{{{hyp=6}}}

then

{{{adj=sqrt(6^2-(- sqrt(5))^2)}}}

{{{adj=sqrt(36-5)}}}

{{{adj=sqrt(31)}}}


then {{{cos(t)=sqrt(31)/6}}} -> with {{{t}}} in quadrant IV, {{{cos(t)}}} is > {{{0}}}


{{{ cos(s + t) =cos(s) cos(t) - sin(s) sin(t)}}}

{{{ cos(s + t) =sqrt(2/3)*(sqrt(31)/6) - (- sqrt(3)/3) (-sqrt( 5)/6)}}}

{{{ cos(s + t) =sqrt(186)/18 - sqrt(15)/18}}}