Question 1197483
{{{sec(t) = 3}}}, terminal point of {{{t }}}is in Quadrant IV


if {{{sec(t) = 3}}},  then {{{cos( t) =1/3 }}} (using identity  {{{cos( t) =1/ sec(t))}}}


using identity {{{sin^2(t)+ cos^2(t)=1}}} calculate {{{sin(t)}}}


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

{{{sin(t)=sqrt(1-(1/3)^2)}}}

{{{sin(t)=sqrt(8/9)}}}

{{{sin(t)=(2sqrt(2))/3}}} or {{{sin(t)=-(2sqrt(2))/3}}}


in Quadrant IV only {{{cos( t)>0}}}
so, take negative value for sin

 {{{cos( t) =1/3}}}

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


{{{tan( t) =-((2sqrt(2))/3)/(1/3)=-2sqrt(2)}}}


{{{cot (t)=(1/3)/(-(2sqrt(2))/3)=-1/2sqrt(2)}}}-> rationalize  {{{cot (t )=-sqrt(2)/4}}}


{{{csc (t )= 1/sin(t)=1/(-(2sqrt(2))/3)=-3/(2sqrt(2))}}}-> rationalize {{{csc (t )=-(3sqrt(2))/4}}}