Course Description The course focuses on the study of trigonometric functions and their applications. It is generally a freshmen level course taken after college algebra and before calculus. Many applications of this course involve the use of trigonometric identities. However we find that establishing identities is quite a difficult topic for most of our students. This may be because there is no numerical answer to these problems and the students haven’t had much experience solving problems that are abstract. The study was conducted at UW-Marshfield, a campus of the UW-Colleges in a 50 minute class period with 19 students.

Executive Summary Our goal was to help students to understand the process of establishing identities and to carry out the process effectively. In establishing an identity, students have to apply a series of logical steps, while always keeping their objective in mind. There is no template problem, no recipe to follow. The steps for establishing an identity are unique to that identity. Our focus was on teaching students what constitutes the proof of an identity and how to present the proof in logical steps. In designing the lesson we tried to link students’ prior knowledge about algebra, in particular algebraic equations and rational equations, with trigonometric functions. To emphasize this we began the lecture by first establishing an algebraic identity, followed by the replacement of the present variable with a trigonometric function to obtain a trigonometric identity. Other examples of identities were then proved on the board with each step being provided by a different student and the underlying algebra underscored by the instructor. Finally the students were given a worksheet with different types of identities to work on as the instructor observed and answered questions. There were six identities on the worksheet. Most students attempted 4 ~ 5 and on average completed the proofs of about 4 identities correctly, using varied approaches. Furthermore, the students displayed enthusiasm and confidence in carrying out their work. This carried over to their performance in the final exam: more students attempted and successfully established the identities compared to previous years, when a majority of the students simply skipped these problems.

Printer Friendly Version of Complete Report Establishing Trigonometric Identities

The Lesson Below are links to the lesson plan and the materials used to teach it. The Lesson Worksheet on Trigonometric Identities

The Study Below are links to the study of the lesson. The Study