about cosine similarity

Question

I am finding cosine similarity between documents.. I did it like this

D1=(8,0,0,1) where 8,0,0,1 are the tf-idf scores of the terms t1, t2, t3 , t4

D2=(7,0,

Answer 1

The denominator is wrong.

The cosine similarity is defined as

         D1 · D2
 sim = ———————————
        |D1| |D2|

Here

D1 · D2 = (7*8 + 0*0 + 0*0 + 1*1) = 57
           ______________________    __
   |D2| = √ 7^2 + 0^2 + 0^2 + 1^2 = √50
           ______________________    __
   |D1| = √ 8^2 + 0^2 + 0^2 + 1^2 = √65

So the similarity should be (57 / √(50 * 65)) = 0.999846142, not 5.