The azimuth limits of the setting Sun ([b]A{/B]) can be calculated from the relationship between the latitude of the observer (phi) and the declination of the Sun at the time of observation (delta). This relationship is expressed by the equation:
cos A = sin (delta) / cos (phi)
So at Perth with a latitude of phi= -31'56: cos (phi) = 0.8487. On the 19th of December delta = -23.80 degrees, thus sin delta = 0.4035. Hence cos A = 0.4035/0.8487 = 0.4754, giving A = 61.61 degrees at Sunrise and 298.39 degrees at Sunset.