A Romp Tour of Trigonometry

Most trigonometry texts are either extremely expensive, shallow, or old and not well suited for current STEM curricula. Hence, the motivation for A Romp Tour of Trigonometry. It has all the topics students need and they are presented in a modern fashion.

This text is designed for students going into Calculus and physics. The trigonometric identities needed for Calculus are emphasized. There is a thorough treatment of polar coordinates. Vectors are addressed, including treatment of the dot product. There are several applications of vectors, such as work and force problems, which will be helpful in physics.

A Romp Tour of Trigonometry also provides a more robust theoretical backing of ideas than most trigonometry texts. Most notably it introduces the geometric study of triangles, including a study of triangle congruence and similarity of triangles. This provides students with a richer foundation on which to analyze trigonometry.

The majority of students learn more easily when first introduced to ideas within a concrete setting as opposed to introducing ideas by providing general principles. Frequently, students don't even look at their books, because their texts approach concepts from a perspective that is too abstract for someone learning the material for the first time. For most students, a general understanding of ideas must be built slowly by means of analyses of specific cases. As a result, the emphasis of this text is teaching by means of examples. Abstract ideas are covered, but new ideas are always reiterated more concretely. Furthermore, the examples provide students with an enriched sense of the mathematics, because they provide intuition and explore more ways to formulate problems.

A Romp Tour of Trigonometry is also unique because it doesn't solve problems the way most books do. Instead, it solves them the way students do: based on core ideas. Formulas are used sparingly, unlike in most math books. For example, A Romp Tour of Trigonometry only uses one formulation of the Law of Cosines. Usually, two formulations are provided, one for side lengths and another for angle measures. It makes solving the problems computationally easier, but almost all students forget all but one formulation voiding the benefit. The approach of this text requires more algebra, but it teaches students to solve problems in a more realistic way.

Problem-solving is a critical component of learning mathematics. More than enough exercises are included for students to obtain a thorough understanding of the material. Furthermore, the problems cover a wide range of difficulty, which means A Romp Tour of Trigonometry will be helpful to trigonometry students at many skill levels.