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Analytical Trigonometry with Applications

Preparation for Calculus Part I

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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.
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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.

About the author

Leslie Elizabeth Buck is a Professor of Mathematics at Suffolk County Community College in Riverhead, New York, United States. She has taught mathematics for over 20 years. She holds a BA in Mathematics from Dowling College in Oakdale, New York, an MS in Mathematics from Adelphi University, Garden City, New York and an MS in Environmental Engineering from Polytechnic University in Brooklyn, New York (now New York University). She is a consultant with the Carnegie Foundation for the Advancement for Teaching and author of the book ‘Algebra is Vital’. When Leslie is not teaching or pursuing various creative endeavors of her choice, she prefers to be running around in remote mountain areas for hours on end with her Siberian Husky Minilla, laughing with her beautiful daughter Elise, swimming in open bodies of water with her silly girlfriends or sleeping under the stars.

About the Author
Leslie

Leslie Elizabeth Buck

Leslie Elizabeth Buck is a Professor of Mathematics at Suffolk County Community College in Riverhead, New York, United States. She has taught mathematics for over 20 years. She holds a BA in Mathematics from Dowling College in Oakdale, New York, an MS in Mathematics from Adelphi University, Garden City, New York and an MS in Environmental Engineering from Polytechnic University in Brooklyn, New York (now New York University). She has consulted with the Carnegie Foundation for the Advancement for Teaching and is author of the virtual, interactive book ‘Algebra is Vital’. Her YouTube channel contains videos that complement her books.

Leslie worked briefly in the field as an Environmental Engineer before dedicating her life to the art of teaching. She interned with the U.S. Air Force during the summer of 1996, assisting with the remediation of jet fuel contamination. She published several papers regarding her research there and during her tenure at Polytechnic University.

Leslie spent over two decades volunteering as a licensed wildlife rehabilitator in the State of New York.

When Leslie is not teaching or pursuing various creative endeavors of her choice, she prefers to be running around in remote mountain areas for hours on end with her Australian Cattle dog Aurora, laughing with her beautiful daughter Elise, swimming in open bodies of water with her silly girlfriends or sleeping under the stars.


Maillacheruvu, K.Y., Buck, L., and Lee, E. Biodegradation potential of Photocatalyzed Surfactact Washwater. Journal of Environmental Science Health, Part B, Vol A36, No. 6, 2001.

Burris, David R., Delcomyn, Carrie A., Deng, Baolin, Buck, Leslie E. and Hatfield, Kirk. Kinetics of Tetrachloroethylene-Reductive Dechlorination Catalyzed by Vitamin B12. Environmental Science and Toxicology (SETAC), January 1998, 17:9:1681-1688.

Maillacheruvu, K.Y., Buck, L., Michalapoulos, A. and Huang, Y.H. Photocatalytic Degradation of Naphthalene and TCE in the Presence of Surfactants. Water Research, 1997.

Modeling of Organohalide Reactions in Aqueous B12/Ti(III) Systems. Air Force Office of Scientific Research, Research and Development Laboratories, 5800 Uplander Way, Culver City, CA, August 1996.

Photocatalytic Degradation of Polynuclear Aromatic Hydrocarbons in the Presence of Different Types of Surfactants. 4th Annual Northeast Regional Student Environmental Conference, Center for Environmental Engineering and Science Technologies, University of Massachusetts at Lowell, April 27, 1996.