Why we use cos with dot and sin for cross

 Due to their value

Cos is use for those products whose valuse is maximum at horizontal (0° ) way, horizontal products can not work at perpendicular called scalers. For example work done doesn't work at 90 degree

Same as sin is use with those products whose maximum value is at perpendicular (90°) they don't work at zero angle called vectors for example (torque) doesn't work at zero degree