What do sin∅ and cos∅ tells us in cross product and dot product I mean what is the significance of them & from where it came ?

Dot product tells you what the projection of one vector onto another is, i.e. how much of one vector is in the same direction as the other. It's purely trigonometry. Cross product can be thought of as telling you how orthogonal they are. Again, the angle comes from trig.