I remember in my first year physics classes, when dealing with a force F we would find the vector's x- and y-components using [tex]F_x=r cos(θ)[/tex] and [tex]F_y=r sin(θ)[/tex] I also remember learning in my mathematics classes about unit vectors, but cannot seem to remember using them to break vectors down into their respective x- and y-components. As such, I thought I'd ask this question: Am I correct in thinking that when using a Cartesian coordinate system to describe a force F, if we find the unit vector for F, are the x- and y- components of this unit vector equivalent to [tex]cos(θ)[/tex] and [tex]sin(θ)[/tex] respectively?
Yes, assuming θ is the angle that F makes with the x-axis. Think about it. F_{x} = |F| cos(θ) F_{y} = |F| sin(θ) To get unit vectors, divide each of the above by its magnitude, |F|.