I think what I'm doing is overkill because all I want to know is when to use sin and cos in the components regarding (isolated) two-dimensional collisions. I'm just showing more content because it might help for context. Also, there are more steps in order to find the final velocity which is why you can see some steps cut off, but I didn't bother posting more pictures of it because I thought it was irrelevant from then on as I am only looking for why sin and cos are used. 1. The problem statement, all variables and given/known data On QUESTION #1 III., why is sin used in the East component and cos used in the North component, when in QUESTION #2 II., a different but ultimately similar question, the sin and cos are switched? Please feel free to click through the images in order for context. Also, how do I know if I should label the components East and North? Why not other compass directions? I hope I'm making some sense :P QUESTION #1 I. http://bayimg.com/image/oajpoaaca.jpg [Broken] II. http://bayimg.com/image/aajajaacb.jpg [Broken] III. http://bayimg.com/image/bajadaacb.jpg [Broken] IV. http://bayimg.com/image/cajaaaacb.jpg [Broken] V. http://bayimg.com/image/cajaoaacb.jpg [Broken] QUESTION #2 I. http://bayimg.com/image/cajcpaacb.jpg [Broken] II. http://bayimg.com/image/dajcmaacb.jpg [Broken] III. http://bayimg.com/image/eajcjaacb.jpg [Broken] 2. Relevant equations N/A 3. The attempt at a solution Looked at sine laws, properties of triangles, and so far I have found nothing I can apply it to. Please forgive me if I'm asking such a simple question.