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Whitney, FSA, MAAA  \nVersion 2.4  \nDecember 17, 2023  \nCopyright 2012-2023, Earl Whitney, Reno NV. All Rights Reserved  \nNote to Students  \nThis Trigonometry Handbook was developed primarily through work with a number of High School and College Trigonometry classes. In addition, a number of more advanced topics have been added to the handbook to whet the student’s appetite for higher level study.  \nOne of the main reasons why I wrote this handbook was to encourage the student to wonder; to ask “what about …” or “what if …”. I find that students are so busy today that they don’t have the time, or don’t take the time, to seek out the beauty and majesty that exists in Mathematics. And, it is there, just below the surface. So be curious and go find it.  \nThe answers to most of the questions below are inside this handbook, but are seldom taught.  \n􀁸 Is there a method I can learn that will help me recall the key points on a unit circle without memorizing the unit circle?  \n􀁸 What’s the fastest way to graph a Trig function?  \n􀁸 Can I convert the sum of two trig functions to a product of trig functions? How about the other way around, changing a product to a sum?  \n􀁸 Is there an easy way to calculate the area of a triangle if I am given its vertices as points on a Cartesian plane?  \n􀁸 Don’t some of the Polar graphs in Chapter 9 look like they have been drawn with a Spirograph? Why is that?  \n􀁸 A cycloid is both a brachistochrone and a tautochrone. What are these and why are they important? (you will have to look this one up, but it is well worth your time)  \n􀁸 What is a vector cross product and how is it used?  \n􀁸 How do the properties of vectors extend to 3 dimensions, where they really matter?  \nAdditionally, ask yourself:  \n􀁸 What trig identities can I create that I have not yet seen?  \n􀁸 What Polar graphs can I create by messing with trig functions? What makes a pretty graph instead of one that just looks messed up?  \n􀁸 Can I come up with a simpler method of doing things than I am being taught?  \n􀁸 What problems can I come up with to stump my friends?  \nThose who approach math in this manner will be tomorrow’s leaders. Are you one of them?  \nPlease feel free to contact me [at](at mathguy.us@gmail.com if you)[ ](at mathguy.us@gmail.com if you)[mathguy.us@gmail.com](at mathguy.us@gmail.com if you)[ if you](at mathguy.us@gmail.com if you) have any questions or comments.  \nThank you and best wishes! Earl  \nCover art by Rebecca Williams, Twitter handle: @jolteonkitty  \nTrigonometry Handbook  \nTable of Contents  \nPage Description  \nChapter 1: Functions and Special Angles  \n7 Introduction  \n8 Angle Definitions  \n9 Function Definitions on the x‐ andy‐ Axes  \n9 Pythagorean Identities  \n9 Sine-Cosine Relationship  \n9 Key Angles in Radians and Degrees  \n9 Cofunctions  \n10 Unit Circle  \n11 Function Definitions in a Right Triangle  \n11 SOH-CAH-TOA  \n11 Trigonometric Functions of Special Angles  \n12 Trigonometric Function Values in Quadrants II, III, and IV  \n13 Problems Involving Trig Function Values in Quadrants II, III, and IV  \n14 Problems Involving Angles of Depression and Inclination  \nChapter 2: Graphs of Trig Functions  \n15 Basic Trig Functions  \n17 Characteristics of Trigonometric Function Graphs  \n19 Table of Trigonometric Function Characteristics  \n20 Sine Function  \n22 Cosine Function  \n24 Tangent Function  \n26 Cotangent Function  \n28 Secant Function  \n30 Cosecant Function  \n32 Application: Simple Harmonic Motion  \nChapter 3: Inverse Trigonometric Functions  \n33 Definitions  \n33 Principal Values and Ranges  \n34 Graphs of Inverse Trig Functions  \n35 Problems Involving Inverse Trigonometric Functions  \nTrigonometry Handbook Table of Contents  \nPage Description  \nChapter 4: Key Angle Formulas  \n37 Angle Addition, Double Angle, Half Angle Formulas  \n38 Examples  \n41 Power Reducing Formulas  \n41 Product-to-Sum Formu","cbCaiqzgkbZ6cpkC","https://ap.wps.com/l/cbCaiqzgkbZ6cpkC","pdf",5487541,114,"English","# Chapter 1: Functions and Special Angles\n## Introduction\n## Angle Definitions\n## Function Definitions on the x- and y- Axes\n## Unit Circle\n## SOH-CAH-TOA\n\n# Chapter 2: Graphs of Trig Functions\n## Basic Trig Functions\n## Characteristics of Trigonometric Function Graphs\n## Sine Function\n## Cosine Function\n## Tangent Function\n## Application: Simple Harmonic Motion\n\n# Chapter 3: Inverse Trigonometric Functions\n## Definitions\n## Principal Values and Ranges\n## Graphs of Inverse Trig Functions\n## Problems Involving Inverse Trigonometric Functions\n\n# Chapter 4: Key Angle Formulas\n## Angle Addition, Double Angle, Half Angle Formulas\n## Power Reducing Formulas\n## Product-to-Sum Formulas\n## Sum-to-Product Formulas\n\n# Chapter 5: Trigonometric Identities and Equations\n## Verifying Identities\n## Solving Trigonmetic Equations\n\n# Chapter 6: Solving an Oblique Triangle\n## Laws of Sines and Cosines\n## The Ambiguous Case\n## Height Comparison Method\n## Butterfly Method\n## Bearings\n\n# Chapter 7: Area of a Triangle\n## Geometry Formula\n## Heron's Formula\n## Trigonometric Formulas\n## Coordinate Geometry Formula\n\n# Chapter 8: Polar Coordinates\n## Conversion between Rectangular and Polar Coordinates\n## Expressing Complex Numbers in Polar Form\n## DeMoivre's Theorem\n\n# Chapter 9: Polar Functions\n## Parts of the Polar Graph\n## Symmetry\n## Graphing Methods\n## Graph Types\n## Converting Between Polar and Rectangular Forms\n## Parametric Equations\n\n# Chapter 10: Vectors\n## Vector Components\n## Dot Product\n## Vector Projection\n## Work\n## Vector Cross Product\n## Vector Triple Products\n\n# Appendices\n## Appendix A-Summary of Trigonometric Formulas\n## Appendix B-Solving The Ambiguous Case-Sine Validity Method\n## Appendix C-Summary of Polar and Rectangular Forms\n## Appendix D-Trigonometry Reference\n## Index","[{\"question\":\"What is the purpose of the Trigonometry Handbook according to the note to students?\",\"answer\":\"It is designed to encourage curiosity and help students find the methods inside the handbook that are seldom taught, including efficient ways to recall key ideas and approach problems creatively.\"},{\"question\":\"How does the handbook support graphing trig functions quickly?\",\"answer\":\"It organizes material around basic trig functions and graph characteristics, then provides dedicated guidance such as function values in quadrants and methods for graphing, including polar graphing techniques.\"},{\"question\":\"What topics are covered for solving oblique triangles?\",\"answer\":\"It covers the laws of sines and cosines, methods for solving based on known information, and a detailed treatment of the ambiguous case with multiple comparison methods and special applications like bearings.\"},{\"question\":\"Which vector operations and applications are included in the handbook?\",\"answer\":\"The handbook includes vector components and properties, dot product and projection, work, and vector cross products, plus vector triple products and worked examples.\"}]","Trigonometry Handbook - Version 2.4 - Prepared by Earl L. Whitney | PDF",1791928762]