/sci/ - Science & Math

Hi guys.
AB' vector (orange) is rotated 30 degree CC to AB''.
AB' vector x and y components are shown in bold red.
AB'' vector x and y components are shown in light blue.

We know
X'' = XCos(α) -YSin(α)
Y" = XSin(α)+YCos(α)


What is the geometric meaning of these individual expression of sum shown above?
What does XCos(α) mean geometrically.
Algebraically it would mean X times Cos(α).
But how it can be perceived in the picture shown?