Question 1203393
If {{{ cos(t) = -2/3 }}}, then {{{ adj/hyp=-2/3 }}}


 find opp

{{{ (-2)^2 + b^2 = 3*2 }}}

{{{ 4 + b^2 = 9 }}}

{{{ b^2 = 5 }}}

{{{ b = sqrt(5) }}}
 

{{{ sin(t) =opp/hyp }}}in quadrant III sin is negative

{{{ sin(t) = -sqrt(5)/3 }}} 
 

 {{{ tan(t)=sin(t)/cos(t)=(-sqrt(5)/3)/( -2/3)=sqrt(5)/2 }}}


{{{ cot(t)=cos(t)/sin(t)=( -2/3)/(-sqrt(5)/3)=2/sqrt(5)=(2sqrt(5))/5 }}}


{{{ sec(t)=1/cos(t)=1/( -2/3)=-3/2 }}}


 {{{ csc(t)=1/sin(t)=1/(-sqrt(5)/3)=- 3/sqrt(5)=-(3 sqrt(5))/5 }}}