angle.py

from math import pi, sqrt, acos, asin, sin, cos

for n in range(0, 360+1, 10):
    x = cos(pi * n / 180)
    y = sin(pi * n / 180)
    r = sqrt(x ** 2 + y ** 2)
    th_cos = 180 * acos(x / r) / pi
    th_sin = asin(y / r)
    if th_sin < 0:
        th_cos = 360 - th_cos
    print('%3d: (%+.2f, %+.2f): %.2f' % (n, x, y, th_cos))