This book, intended for a graphing calculator optional trigonometry course, offers students the content and tools they will need to successfully master trigonometry. The authors have addressed the needs of students who will continue their study of mathematics, as well as those who are taking trigonometry as their final mathematics course. Emphasis is placed on exploring mathematical concepts by using real date, current applications and optional technology.
(Each chapter ends with a Summary, Chapter Review Exercises, and a Chapter Test.)
1. The Trigonometric Functions.
Basic Concepts. 2. Acute Angles and Right Triangles.
Angle Relationships and Similar Triangles.
Definitions of the Trigonometric Functions.
Using the Definitions of the Trigonometric Functions.
Trigonometric Functions of Acute Angles. 3. Radian Measure and the Circular Functions.
Trigonometric Functions of Non-Acute Angles.
Finding Trigonometric Function Values Using a Calculator.
Solving Right Triangles.
Further Applications of Right Triangles.
Applications of Radian Measure.
Circular Functions of Real Numbers.
Linear and Angular Velocity.
4. Graphs of the Circular Functions.
Graphs of the Sine and Cosine Functions. 5. Trigonometric Identities.
Translations of the Graphs of the Sine and Cosine Functions.
Graphs of the Other Circular Functions.
Fundamental Identities. 6. Inverse Trigonometric Functions and Trigonometric Equations.
Verifying Trigonometric Identities.
Sum and Difference Identities for Cosine.
Sum and Difference Identities for Sine and Tangent.
Inverse Trigonometric Functions. 7. Applications of Trigonometry and Vectors.
Trigonometric Equations I.
Trigonometric Equations II.
Equations Involving Inverse Trigonometric Functions.
Oblique Triangles and the Law of Sines. 8. Complex Numbers, Polar Equations, and Parametric Equations.
The Ambiguous Case of the Law of Sines.
The Law of Cosines.
Vectors and the DOT Product.
Applications of Vectors.
Complex Numbers. 9. Exponential and Logarithmic Functions.
Trigonometric (Polar) Form of Complex Numbers.
Product and Quotient Theorems.
Powers and Roots of Complex Numbers.
Polar Equations and Graphs.
Parametric Equations, Graphs, and Applications.
Exponential Functions. Answers to Selected Exercises. Index. Index of Applications.
Evaluating Logarithms and the Change-of-Base Theorem.
Exponential and Logarithmic Equations.