Question 730564
{{{tan(theta)=opp/adj=-3/1}}}

so

{{{hyp=sqrt(1^2+(-3)^2)=sqrt(10)}}}

so 

{{{sin(theta)=(3*sqrt(10))/10}}}

{{{cos(theta)=-sqrt(10)/10}}} (we take the negative case because cosine is negative for this example)

now 

{{{tan(theta/2)=sin(theta)/(1+cos(theta))}}}

Therefore...


{{{tan(theta/2)=((3*sqrt(10))/10)/(1-sqrt(10)/10)}}}

which simplifies to

{{{(sqrt(10)+1)/3}}}