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Python - math.atan2() method example

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Created by:

Faith-W

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The math.atan2() function returns the angle in radians in the range -math.pi/2 to +math.pi/2 between the positive x-axis and the ray to the point (x, y) ≠ (0, 0).

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import math
​
#                y    x         angle in radians
print(math.atan2(2,   4))     # 0.4636476090008061  <-   ~26.6 degrees
print(math.atan2(4,  -2))     # 2.0344439357957027  <-  ~116.6 degrees
print(math.atan2(-2, -4))     # -2.677945044588987  <- ~-153.4 degrees
print(math.atan2(-4,  2))     # -1.1071487177940904 <-  ~-63.4 degrees

atan2() method has been visualized on below image:

atan2(y, x) function visualization - Python math module. — Atan2(y, x) function visualization - Python math module.

1. Documentation

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Syntax	xxxxxxxxxx 1 math.atan2(y, x)
Parameters	`y`, `x` - double values that are coordinates of the point.
Result	`number` value of the angle between two lines `OP` and `OX` in radians in the range `-math.pi/2` to `+math.pi/2`. Where: `O=(0, 0)` - intersection point of coordinate system axes, `P=(x, y)` - out point, `OX` - positive part of x-axis. If point is in the 1st (I) or 2nd (II) quadrant angle is measured in a counterclockwise direction. If point is in the 3rd (III) or 4th (IV) quadrant angle is measured in a clockwise direction. Note: angle arrows show measured angles for points located in different quadrants.
Description	`atan2` is a method that takes two parameters and returns an approximation of the arctangent(y/x) function taking into account quadrants of a point location (`P=(x, y)`).

2. Working with degrees

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import math
​
​
def calculate_angle(x, y):
    angle = math.atan2(x, y)
    return (180 / math.pi) * angle
​
​
#                     y    x       degrees
print(calculate_angle(2,   4))   # 26.56505117707799
print(calculate_angle(4,  -2))   # 116.56505117707799
print(calculate_angle(-2, -4))   # -153.434948822922
print(calculate_angle(-4,  2))   # -63.43494882292201

3. Conversion to only clockwise angles in degrees

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This section shows how to convert angles to clockwise angles (from 0 to 360 degrees).

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import math
​
​
def calculate_angle(x, y):
    angle = math.atan2(x, y)
​
    if angle < 0:
        angle += 2 * math.pi
    return (180 / math.pi) * angle
​
​
#                     y    x        degrees
print(calculate_angle(2,   4))    # 26.56505117707799
print(calculate_angle(4,  -2))    # 116.56505117707799
print(calculate_angle(-2, -4))    # 206.565051177078
print(calculate_angle(-4,  2))    # 296.565051177078
​

4. Conversion to only counterclockwise angles in degrees

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This section shows how to convert angles to counterclockwise angles (from -360 to 0 degrees).

xxxxxxxxxx
 
import math
​
​
def calculate_angle(x, y):
    angle = math.atan2(x, y)
​
    if angle > 0:
        angle -= 2 * math.pi
    return (180 / math.pi) * angle  # rad to deg conversion
​
​
#                     y   x        degrees
print(calculate_angle(2,   4))    # -333.434948822922
print(calculate_angle(4,  -2))    # -243.434948822922
print(calculate_angle(-2, -4))    # -153.434948822922
print(calculate_angle(-4,  2))    # -63.43494882292201

References

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Python - math.atan2() method example

1. Documentation

2. Working with degrees

3. Conversion to only clockwise angles in degrees

4. Conversion to only counterclockwise angles in degrees

References

Python - math module

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