Why does my implementation of the Great Circle distance formula give wrong results?

Question

I'm trying to implement algorithm which will calculate distance between 2 points using great circle distance formula according to guide

My function:

from math import sin, cos, radians


def get_great_circle_distance(first_coords, second_coords, radius):
    """
    :param first_coords: (first_client_latitude, first_client_longitude) <- degrees
    :param second_coords: (second_client_latitude, second_client_longitude) <- degrees
    :param radius: planet radius
    :return: distance
    """

    la_1, lo_1 = map(radians, first_coords)
    la_2, lo_2 = map(radians, second_coords)

    denominator = cos(
        cos(la_1) * cos(la_2) * cos(lo_1 - lo_2) +
        sin(la_1) * sin(la_2)
    )
    distance = radius / denominator

    return distance

For example I call: distance = get_great_circle_distance((55, 28), (86, 70), 7) and expecting ~3.93km, but I get 10.56897.

Answer 1

The linked formula uses cos^-1 which means the inverse of the cosine function. cos^-1(x) is not the same as 1/cos(x).

It is also known as arccos. In Python it is called acos.