If tan(theta) = 3/4 and sin(theta) < 0 how do you find cos(theta)?

If ##tan theta = 3/4## and ##tan theta = (opposite side)/(adjacent side) = a/b##
then ## a = 3 b = 4##
solve for the hypotenuse side
##c^2 = a^2+b^2##
##c^2 = 3^2 + 4^2##
##c = sqrt(9 + 16)##
##c = 5##
For ##cos theta = (adjacent side)/(hypotenuse) = b/c##
##cos theta = 4/5## >>> Answer