Question 378975
If sin(theta) = -1/5 then by the Pythagorean identity,

{{{(-1/5)^2) + cos^2(theta) = 1}}}

{{{cos^2 (theta) = 24/25}}}

{{{cos(theta) = (2*sqrt(6))/5}}} (plus or minus)

However, since tan(theta) < 0 and sin(theta) < 0, it follows that cos (theta) > 0 because {{{sin(theta)/cos(theta) = tan(theta)}}} by definition. Therefore we take the positive value of cos(theta), or {{{(2sqrt(6))/5}}}.