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From the docs :
Calculates the angle (in radians) from a specified point to the coordinate origin as measured from the positive x-axis. Values are returned as a float in the range from PI to -PI. The atan2() function is most often used for orienting geometry to the position of the cursor. Note: The y-coordinate of the point is the first parameter, and the x-coordinate is the second parameter, due the the structure of calculating the tangent
The inverse of tan(), returns the arc tangent of a value. This function expects the values in the range of -Infinity to Infinity (exclusive) and values are returned in the range -PI/2 to PI/2
I'm not too sure what the real difference is here though. I get that atan2() is generally used instead of atan() for movement, and I've seen it work better, but I don't really understand why this is.
Can anyone explain further please?