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