Question

Why is the formula of work is F. S. $cos\theta$?

Answer 1

Work done in physics is defined as a dot product of force vector and displacement vector.
W = F.S.cos $\theta$
where cos $\theta$ is the angle between the force vector and displacement vector.
when a person pushes a box with force F and the box moves a distance S in the direction of the force applied then the angle between F and S is 0.
cos (0) = 1
therefore W = F.S
but if we had used sin (0) = 0
W = F . S . 0 = 0
but there is some work done hence using sin will give you an incorrect answer.