The trig table we memorize in high school only includes the angles 0, 30, 45, 60, and 90 degrees. Why those angles and not others? If we were to add some more angles to the table, which ones should we add? It turns out that we can answer these questions using a little Galois theory. The goal of the Expositions in Algebra lecture series is to acquaint students and faculty with the algebra studied here at Emory. Each talk will present interesting and advanced algebra at a level accessible to a student currently enrolled in the first-year graduate algebra sequence.