Confusion about momentum question

[dark-ryder341]

Homework Statement

Hmm, well, this isn't an actual homework question. It's more of a general one, but it does apply to homework. What I want to know is, for momentum, how do you know when to use sine and cosine for vectors? Likeeee, let me show you an example of what I mean:

This is a depiction of the following: two hockey players approach each other at an angle with different speeds. mass(m1)=90kg, velocity(v1)=10 m/s; (m2)=100kg, (v2)=15 m/s. They collide and stick together. The question asks to find the final velocity of the two.

Homework Equations

pi = m1v1i + m2v2i
pf = m1v1f + m2v2f >>> (m1+m2)vf

The Attempt at a Solution

Now, here's the beginning of how it's solved, according to my teacher.

pi = (90+10)i + 100(15cos(theta)i(hat) + 15sin(theta)j(hat)) = (900+1300)i(hat) + 750j(hat)

I'm going to stop here, as this is what I don't understand. How did he figure out that he should use 15cos(theta) and 15sin(theta) rather than just 15 m/s? And how did he know that i(hat) was using cosine, rather than sine? If you understand what I mean...I'm just not sure where the cos and sin, came from, in other words, and how he knew what order it went in. There is another question in my book where it's switched - i(hat) is sine and j(hat) is cosine.

Thanks for any help!

 

[rl.bhat]

First of all select x and y axis. In the given problem v1 is along x-axis with i as the unit vector. j is the unit vector along y-axis.
pi = m1v1*i + m2v2*cosθ*i + m2v2*sinθ*J
If A and B are the two vectors with an angle θ between them, then the component of B along A is B*cosθ and component perpendicular to A is B*sinθ. Same principle is used in the above problem.