Question 323906
{{{sin(theta)=-5/13}}}
You also know that,
{{{(cos(theta))^2+(sin(theta))^2=1}}}
{{{(cos(theta))^2+(-5/13)^2=1}}}
{{{(cos(theta))^2+25/169=1}}}
{{{(cos(theta))^2=1-25/169}}}
{{{(cos(theta))^2=144/169}}}
{{{cos(theta)=0 +- 12/13}}}
Now look at the range you're considering,
({{{3*pi/2}}},{{{2pi}}}) or the fourth quadrant.
In that quadrant, the cosine is positive, the sine is negative.
{{{cos(theta)=12/13}}}