What is the graph of $\theta = \frac{\pi} {3}$? In our calculus exam, we were asked to identify the graph of this equation. My answer was "straight line" and I was wrong, and I still haven't got the chance to ask my instructor as to why my answer was incorrect. But I would love to know why. I'm pretty sure that the graph of theta = pi is a straight line, so why not $\theta = \frac{\pi}{3}$ as well?

Hayden is correct.  The graph is a ray extending from the origin into the first quadrant, which makes an angle of $\pi/3$ with the positive $x$-axis.
See the graphic at the beginning of this article:
http://en.wikipedia.org/wiki/Polar_coordinate_system
Once we extend the ray into a complete line, then the portion of the line in the third quadrant is making an angle of $4\pi/3$ with the positive $x$-axis.
