This dissertation reports the results of a qualitative research project that aimed to develop a research-based perspective on the purpose of trigonometry in the modern sciences. The investigation was guided by three objectives. First, the study sought to identify the purpose of trigonometry as described by educators and high school textbooks. Second, the research investigated the perspectives these sources held about definitions of the trigonometric functions. Third, the investigation examined the potential benefits and drawbacks of a line-segment definition of the trigonometric functions. The study followed a grounded theory methodology with data collection and analysis intertwined. Participants included faculty from two large Midwestern research universities, high school teachers, and authors of standards documents. Textbooks were drawn from introductory algebra, geometry, advanced algebra, precalculus, and calculus texts. Data collected included surveys, interviews, and textbook excerpts. Analysis used the constant comparative method (Corbin & Strauss, 2008; Glaser & Strauss, 2006/1967). Analysis resulted in the emergence of a grounded theory, the tensions of trigonometry, which described three interrelated themes within the data: definition, application, and role. Two ideas emerged that connected the tensions of trigonometry, the regions of interaction, which described the interplay between the three tensions, and the idealized dichotomy of trigonometry education, which outlined opposing perspectives on trigonometry: trigonometry for all and trigonometry for some. The grounded theory outlines a range of competing purposes for trigonometry in the modern sciences. It suggests that educators are engaged in a process of continual negotiation that results in the formation of a localized purpose of trigonometry. The benefits and drawbacks of different definitions are not based on mathematical sophistication, but are situational. Furthermore, the theory suggests that the line-segment definition faces a number of obstacles if it is to be adopted. Implications for future research on the teaching and learning of trigonometry are discussed. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]