Question 1063064
{{{tan(x)=-1/2}}}
{{{tan^2(x)+1=sec^2(x)}}}
{{{sec^2(x)=1/4+1}}}
{{{sec^2(x)=5/4}}}
{{{1/cos^2(x)=5/4}}}
{{{cos^2(x)=4/5}}}
{{{cos(x)=0 +- 2/sqrt(5)}}}
Since we know {{{cos(x)<0}}},
{{{cos(x)=-(2/5)sqrt(5)}}}