Much of our understanding of vectors will come from understanding triangles.  Triangles can be found inside circles... if you draw a radius to a point on a circle, you can draw a line from that point to the X axis and/or the Y axis.
Here we have created 2 triangles.  If the circle were made larger, the triangles created would still be the same shape.  This means that there are certain things about these triangles will always stay the same, like the ratio of one particular side to another.  These ratios have terms like "sine" and "cosine".

Without going into all of the history and trigonometry, we can get several useful tools from this simple understanding of a triangle...

EXAMPLE: The "sine" of the angle marked "q" equals the opposite side divided by the hypotenuse. To remember the formulae, just memorize this mnemonic: SOH-CAH-TOA

If I walk 3 blocks along the X axis, then 4.5 blocks up the Y axis , what angle would be made with the X axis?  NOTE: the diagram just above shows this problem!
In this problem I have 2 sides and no angles, and I want the angle marked q.
Notice the equation tanq=opp/adj, fill in the known numbers...

tanq = 4.5/3 = 1.5,  so  tanq = 1.5... almost done...

to get the "q" term by itself, we multiply by the reciprocal... something your calculator does automatically when you hit [shift or inv or 2nd] then "tan";

More simply, you'd press these keys... [1.5] [shift or inv or 2nd] [tan]= 56.3°