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Trigonometry Through Wayfinding and Navigation Across the Pacific
Kamuela E Yong
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Front Matter
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Colophon
Dedication
Acknowledgements
Preface
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Core Standards
1
Trigonometric Functions
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1.1
Pacific Island Navigation
1.1.1
Micronesia
1.1.2
Hawaiʻi
1.1.3
Marshall Islands
1.1.4
Elsewhere in the Pacific
1.1.5
Exercises
1.2
Angles and Their Measure
1.2.1
Degree
1.2.2
Radian
1.2.3
Arc Length
1.2.4
Area of a Sector of a Circle
1.2.5
Angular Velocity and Linear Speed
1.2.6
Exercises
1.3
Unit Circle
1.3.1
Unit Circle
1.3.2
Trigonometric Functions
1.3.3
Trigonometric Functions of an Angle
1.3.4
Symmetry on the Unit Circle
1.3.5
Trigonometric Functions on a Circle with Radius
r
1.3.6
Exercises
1.4
Right Triangle Trigonometry
1.4.1
Trigonometric Ratios
1.4.2
Special Triangles
1.4.3
Cofunctions
1.4.4
Using a Calculator
1.4.5
Solving Right Triangles
1.4.6
Solving Applied Problems
1.4.7
Exercises
1.5
Trigonometric Functions of Any Angle
1.5.1
Determine the Signs of the Trigonometric Functions Based on the Quadrant
1.5.2
Reference Angles
1.5.3
Evaluating Trigonometric Functions Using Reference Angles
1.5.4
Periodic Functions
1.5.5
Trigonometric Table
1.5.6
Pythagorean Identities
1.5.7
Even and Odd Trigonometric Functions
1.5.8
Exercises
2
Graphs of the Trigonometric Functions
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2.1
Graphs of the Sine and Cosine Functions
2.1.1
Domain and Range of Sine and Cosine
2.1.2
The Sine Function
2.1.3
The Cosine Function
2.1.4
Graphing Transformations of Sine and Cosine
2.1.5
Exercises
2.1.6
References
2.2
Graphs of Other Trigonometric Functions
2.2.1
Domains of the Tangent and Cotangent Functions
2.2.2
Ranges of the Tangent and Cotangent Functions
2.2.3
Domains of the Cosecant and Secant Functions
2.2.4
Ranges of the Cosecant and Secant Functions
2.2.5
The Tangent Function
2.2.6
The Cotangent Function
2.2.7
The Cosecant Function
2.2.8
The Secant Function
2.2.9
Graphing Transformations of Other Trigonometric Functions
2.2.10
Exercises
2.3
Sinusoidal Curve Fitting and Graphical Analysis
2.3.1
Finding Sinusoidal Equations from Characteristics
2.3.2
Finding Sinusoidal Equations from Graphs
2.3.3
Finding Sinusoidal Equations from Data
2.3.4
Finding Sinusoidal Equations with Technology
2.3.5
Exercises
2.4
Inverse Trigonometric Functions
2.4.1
Inverse Trigonometric Functions
2.4.2
Finding the Exact Value of an Inverse Trigonometric Function
2.4.3
Approximations of Inverse Trigonometric Functions
2.4.4
Graphs of Inverse Trigonometric Functions
2.4.5
Composition of Inverse Trigonometric Functions
2.4.6
Exercises
3
Analytic Trigonometry
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3.1
Trigonometric Identities
3.1.1
Fundamental Trigonometric Identities
3.1.2
Simplifying Trigonometric Expressions
3.1.3
Verifying Trigonometric Identities
3.1.4
Exercises
3.2
Addition and Subtraction Formulas
3.2.1
Addition and Subtraction Formulas for Cosine
3.2.2
Addition and Subtraction Formulas for Sine
3.2.3
Addition and Subtraction Formulas for Tangent
3.2.4
Cofunction Identities
3.2.5
Sums of Sines and Cosines
3.2.6
Summary
3.2.7
Exercises
3.3
Double-Angle and Half-Angle Formulas
3.3.1
Double-Angle Formulas
3.3.2
Reducing Powers Formulas
3.3.3
Half-Angle Formulas
3.3.4
Exercises
3.4
Product-to-Sum and Sum-to-Product Formulas
3.4.1
Product to Sum Formulas
3.4.2
Sum to Product Formulas
3.4.3
Exercises
3.5
Basic Trigonometric Equations
3.5.1
Solving Equations with a Single Trigonometric Function
3.5.2
Solving Trigonometric Equations with Square Terms
3.5.3
Solving Trigonometric Equations by Factoring
3.5.4
Solving a Trigonometric Equation with a Calculator
3.5.5
Exercises
3.6
Trigonometric Equations - Advanced Techniques
3.6.1
Solving a Trigonometric Equation by Using Fundamental Identities
3.6.2
Solving a Trigonometric Equation with Multiples of an Angle
3.6.3
Solving a Trigonometric Equation with a Graphing Utility
3.6.4
Exercises
4
Applications of Trigonometry
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4.1
The Law of Sines
4.1.1
Law of Sines
4.1.2
Solving ASA Triangles
4.1.3
Solving SAA Triangles
4.1.4
Solving SSA Triangles: The Ambiguous Case
4.1.5
Area of an oblique triangle
4.1.6
Exercises
4.2
The Law of Cosines
4.2.1
Law of Cosines
4.2.2
Using Law of Cosines (SAS)
4.2.3
Using Law of Cosines (SSS)
4.2.4
Area of an oblique triangle
4.2.5
Exercises
4.3
Geometric Vectors
4.3.1
Geometric Vectors
4.3.2
Equivalent Vectors
4.3.3
Vector Addition
4.3.4
Multiplying Vectors by a Scalar
4.3.5
Vector Subtraction
4.3.6
Velocity
4.3.7
Exercises
4.4
Coordinate Vectors
4.4.1
Vectors in Coordinates
4.4.2
Properties of Addition, Length, and Scalar Multiplication
4.4.3
Finding a Unit Vector
4.4.4
Vector Components and Direction
4.4.5
Velocity
4.4.6
Exercises
Back Matter
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Bibliography
A
An Introduction to the Canoes in This Book
A.1
Alingano Maisu
A.2
Faʻafaite
A.3
Gaualofa
A.4
Haunui
A.5
Hawaiʻiloa
A.6
Hinemoana
A.7
Hōkūleʻa
A.8
Kānehūnāmoku
A.9
Mānaiakalani
A.10
Marumaru Atua
A.11
Paikea
A.12
Te Matau a Māui
A.13
Uto ni Yalo
A.14
Vaka Moana
Glossary (Math)
Glossary (Canoe and Wayfinding)
Index
Section
A.2
Faʻafaite
Faʻafaite is a double-hulled voyaging canoe built in 2009. It is one of eight vaka moana built for the Okeanos Foundation for the Sea. It is owned by the Faʻafaite - Tahiti Voyaging Society.
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