Can you provide a visual description of the sun rise? The Sun rises in the east only two times a year. The other days, the Sun rises in the east, but a little bit to the north, or to the south. How can you know the degree of how much north or south it is? Does it vary in different hemispheres?
Elaborating on the answer from James K, the azimuth of the sunrise depends on the declination of the Sun and the observer's latitude. The declination ranges between approximately +23.4 to -23.4 and depends on the date. 
$$\cos(\theta_R)=-\frac{\sin(declination)}{\cos(latitude)}$$

where $\theta_R$ is the angle measured around the horizon from due south to the location where the object rises or sets. From this formula, the azimuth of rising is due east when the declination is 0 which occurs on the spring and autumnal equinoxes.

The calculation of the Sun's declination is not too involved, but it is longer than I want to type at the moment. Since the declination does not change very much from year to year, it would be relatively easy to pick a few dates throughout the year, get the declination for those dates, and calculate the azimuth. 

Also see the following question: Solar azimuth for celtic fire festivals