we take sin component in cross product and Cos component in dot or scalar product in vectors because sin is related to vertical component whose mathematical formula is perpendicular divided by hypotenuse which seems that it is a perpendicular that is a vertical component where as we can see similar in the case of Cos is mathematical formula is base divided by hypotenuse so we take cos component as horizontal one in vectors..... hope this helps you....
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Answer:
sin is taken as a cross product because sin is actually related with vertical component and cos is related with horizontal component .
e.g in case of sin ,all the three quantities taken are being necessary mutuallly perpendicular to each other .
we take sin component in cross product and Cos component in dot or scalar product in vectors because sin is related to vertical component whose mathematical formula is perpendicular divided by hypotenuse which seems that it is a perpendicular that is a vertical component where as we can see similar in the case of Cos is mathematical formula is base divided by hypotenuse so we take cos component as horizontal one in vectors..... hope this helps you....