Trigonometry

The text presents a circular function approach to trigonometry by demonstrating connections between the familiar algebra and the new language of trigonometry. This method, along with foreshadowing, is used throughout the text to provide students with a comfortable base for learning something new from something old or familiar. With just a few connections to algebra, students have the tools to understand the circular functions, their domains and ranges, and the relationship between the circular functions and the functional values. The approach immediately launches the student into the concept of periodic functions, their applications, graphs, and use in modeling many periodic phenomena. Beginning with this approach provides the student with a common thread that can be used to discover, connect and understand the remaining concepts of trigonometry.

Circular Functions. The Coordinate Plane, Graphing and Solving Equations. The Circular Functions. Functional Values for Common Arcs. Reference Arcs and Circular Functional Values. Four Additional Circular Functions. Negative Identities and Periods for the Circular Functions. Graphs of Circular Functions. Graphs of the Sine and Cosine Functions. Period, Phase Shift (horizontal shift) and other Translations. Applications and Modeling with Sinusoidal Functions. Graphs of the Tangent, Cotangent, Secant and Cosecant Functions. Inverses of the Circular Functions. The Trigonometric Functions. Angles and Measurement Units - Radians and Degrees. Trigonometric and Circular Functions. Solving Right Triangles. Solution of Triangles - Law of Sines. Solution of Triangles - Law of Cosines. Identities. Proving Identities. Sum and Difference Identities for Cosine. Sum and Difference Identities for Sine and Tangent. Double-Angle Identities. Half-Angle and Additional Identities. Solving Trigonometric Equations. Solving Conditional Equations. More Trigonometric Equations, Multiple Angle Equations. Parametric Equations. Vectors, Polar Equations, and Complex Numbers. Geometric Vectors and Applications. Algebraic Vectors. Polar Coordinate System. Complex Numbers. Trigonometric Form for Complex Numbers.