Question 1097963
In quadrant IV, cosine (and secant) are positive,
but,since,and tangent are negative.
{{{sec(theta)=1/cos(theta)=12/5}}} ---> {{{cos(theta)=5/12}}}
For all angles, {{{cos^2(theta)+sin^2(theta)=1}}} ,
so {{{(5/12)^2+sin^2(theta)=1}}} --> {{{25/144+sin^2(theta)=1}}} --> {{{sin^2(theta)=1-25/144=(144-25)/144=119/144}}} ,
and because {{{sin(theta)}}} is a negative number in quadrant IV,
{{{sin(theta)=-sqrt(119/144)=-sqrt(119)/12}}} .
Then, because for any angle {{{tan(theta)=sin(theta)/cos(theta)}}} ,
{{{tan(theta)=(sqrt(119)/12)/(5/12)=(sqrt(119)/12)(12/5)=highlight(sqrt(119)/5)}}} .