Firstly, to find the degree, the function must be polynomial in that variable. And $F(x,y) =cos(y/x)$ is not polynomial in x,y though it can be proved homogeneous.
proof of homogeneous: $F(λx,λy)=cos(λy/λx)=(λ^0)(cos(y/x))=(λ^0)F(x,y)$ degree given in book is 0.