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Analytical Trigonometry with Applications

Preparation for Calculus Part I

192
Language:  English
These books are intended to prepare a student for a first course in Calculus after completing a study of intermediate algebra and basic functions.
Content
Description
1. Basic Definitions and Theorems
1. Angle Measurement and Arc Length
2. The Pythagorean Theorem
3. Right Triangle Trigonometry
4. Fundamental Trigonometric Identities
2. Graphs of Trigonometric Functions
1. Domain and Range of a Trigonometric Function
2. Graphs of Sinusoidal Functions
3. Graphs of Tangent, Cotangent, Secant and Cosecant
4. Transformations of the Graphs of Trigonometric Functions
5. Inverse Trigonometric Functions
3. Trigonometric Identities and Equations
1. Review of Fundamental Trigonometric Identities
2. Sum and Difference of Angles Identities
3. Double- and Half-Angle Identities
4. Product-to-Sum and Sum-to-Product Identities
5. Solving Trigonometric Equations
4. Applications of Trigonometry
1. Right Triangle Trigonometry
2. The Law of Sines
3. The Law of Cosines
4. The Area of a Triangle
5. Endnotes
6. Index

These books are intended to prepare a student for a first course in Calculus after completing a study of intermediate algebra and basic functions. Part I begins with a review of basic trigonometry and continues with analytic trigonometry and applications. Part II deals with polar functions, an introduction to the complex plane, conic sections, systems of equations and ends with an introduction to sequences. Companion videos are included throughout with web links and QR codes that enable hardcopy access to these videos.