Add coordinate systems conversions (TheAlgorithms#2510)

Author: the-kaustubh

Diff for: maths/coordinate_conversion.py

@@ -0,0 +1,45 @@
+""" Co-ordinate conversion """
+
+from math import sin, cos, atan
+
+def polar_to_cartesian(radius: float, angle: float) -> (float, float):
+    """
+    This function returns (x, y) i.e. cartesian co ordinates
+    given polar coordinates (r, theta)
+    Reference:
+    https://en.wikipedia.org/wiki/Polar_coordinate_system
+    https://en.wikipedia.org/wiki/Cartesian_coordinate_system
+
+    >>> polar_to_cartesian(0, 0)
+    (0.0, 0.0)
+    >>> polar_to_cartesian(1, 0.7853981633974483)
+    (0.7071067811865476, 0.7071067811865475)
+    """
+    x_coordinate = radius * cos(angle)
+    y_coordinate = radius * sin(angle)
+    return (x_coordinate, y_coordinate)
+
+def cartesian_to_polar(x_coordinate: float, y_coordinate : float) -> (float, float):
+    """
+    This function returns (r, theta) i.e. cartesian co ordinates
+    given polar coordinates (x, y)
+    Reference:
+    https://en.wikipedia.org/wiki/Polar_coordinate_system
+    https://en.wikipedia.org/wiki/Cartesian_coordinate_system
+
+    >>> cartesian_to_polar(0, 0)
+    (0.0, inf)
+    >>> cartesian_to_polar(0.7071067811865476, 0.7071067811865475)
+    (1.0, 0.7853981633974483)
+
+    """
+    radius = ((x_coordinate ** 2) + (y_coordinate ** 2)) ** 0.5  # root of x squared and y squared
+    theta  = atan( y_coordinate / x_coordinate ) if (x_coordinate != 0) else float("inf")
+    return (radius, theta)
+
+def main():
+    import doctest
+    doctest.testmod()
+
+if __name__ == '__main__':
+    main()