Graphing polar curves typically involves a combination of three traditional techniques, all of which can be time-consuming and tedious. However, an alternative method--graphing the polar function on a rectangular plane--simplifies graphing, increases student understanding of the polar coordinate system, and reinforces graphing techniques learned earlier in trigonometry. This article looks first at traditional techniques and then introduces this alternative method that both incorporates and improves on these. This increased understanding allows students to explore and discover fundamental properties of the polar system that may be too difficult otherwise.