How do I find the angle between 2 points in pygame?

Question

I am writing a game in Python with Pygame.
The co-ords (of my display window) are
( 0 , 0 ) at the top left and
(640,480) at the bottom right.

The angle is
0° when pointing up,
90° when pointing to the right.

I have a player sprite with a centre position and I want the turret on a gun to point towards the player. How do I do it?
Say,
x1,y1 are the turret co-ords
x2,y2 are the player co-ords
a is the angle's measure

Answer 1

First, math has a handy atan2(denominator, numerator) function. Normally, you'd use atan2(dy,dx) but because Pygame flips the y-axis relative to Cartesian coordinates (as you know), you'll need to make dy negative and then avoid negative angles. ("dy" just means "the change in y".)

from math import atan2, degrees, pi
dx = x2 - x1
dy = y2 - y1
rads = atan2(-dy,dx)
rads %= 2*pi
degs = degrees(rads)

degs ought to be what you're looking for.

Answer 2

Considering a triangle

sin(angle)=opposed side / hypotenuse