# Unit Vectors and Vector Components

by Alexrey
Tags: components, unit, vector, vectors
 P: 34 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 $$F_x=r cos(θ)$$ and $$F_y=r sin(θ)$$ 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 $$cos(θ)$$ and $$sin(θ)$$ respectively?
Mentor
P: 21,402
 Quote by Alexrey 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 $$F_x=r cos(θ)$$ and $$F_y=r sin(θ)$$ 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 $$cos(θ)$$ and $$sin(θ)$$ respectively?
Yes, assuming θ is the angle that F makes with the x-axis.