
Make: Trigonometry
Beschreibung
Weitere Details
Weitere Ausgaben
Inhalt
- Cover
- Copyright
- Table of Contents
- Preface
- Who This Book Is For
- Teaching and Learning with This Book
- What You Will Need
- Acknowledgments
- About the Authors
- Chapter 1. Trigonometry and Analytic Geometry
- Trigonometry
- Analytic Geometry
- Structure of This Book
- Math Concepts to Know
- Chapter Key Points
- Chapter 2. 3D Printed Models
- OpenSCAD
- OpenSCAD Workflow
- Navigating on the Screen
- Comments
- Idiosyncrasies of OpenSCAD
- The Models
- Example 1: Changing a Parameter
- Example 2: Changing a Model with the Customizer
- Downloading the Models: Github
- Some Models Have Small Parts
- 3D Printing
- 3D Printing Workflow
- Materials
- Printing Tips
- If You Do Not Have a 3D Printer
- Chapter Key Points
- Terminology and Symbols
- References
- Chapter 3. Triangles and Trigonometry
- Angles of a Triangle
- Degrees, Radians, and Pi
- Prove Triangle Angles Add to 180°
- How to Use a Protractor
- Drawing and Labeling Triangles
- Congruent Triangles
- Similar Triangles
- Trigonometry Basics
- Pythagorean Theorem
- Squares and Square Roots
- Pythagoras' LEGO Bricks
- Sine, Cosine, Tangent
- Hypotenuse Model
- Complementary Angles
- Other Ratios
- Angles Greater Than 90°
- Finding the Length of a Side
- Arcsin, Arccos, Arctan
- Calculating with Sine and Cosine
- Measure Something Big
- Testing with a Known Object
- Garage Roof Height
- Chapter Key Points
- Terminology and Symbols
- References
- Answers
- Hypotenuse Model
- Calculating with Sine and Cosine
- Chapter 4. Coordinate Systems and Analytic Geometry
- Analytic Geometry
- Coordinate Systems
- Coordinate System Model
- Model Parameters
- Cartesian Coordinates
- Graphing a Line
- 3D Coordinates
- Polar Coordinates
- Cylindrical Coordinates
- Spherical Coordinates
- Making Curves and Surfaces
- Craft Materials Models
- 3D Printed Models
- Chapter Key Points
- Terminology and Symbols
- Chapter 5. The Unit Circle
- Beyond the Right Triangle
- Angles Between 90° and 180°
- Angles Between 180° and 270°
- Angles Between 270° and 360° (or -90° and 0°)
- Principal Value
- The Unit Circle
- Making 3D Printed Models
- Sine Versus Cosine
- Rolling Out a Sine Curve
- Phase
- Frequency
- Amplitude
- Angular Frequency
- Period
- Paper Models
- Graphing Trig Functions
- Graphing Sinusoids in Cartesian Coordinates
- Polar Graphs of Sinusoids
- Graphing in Radians
- Chapter Key Points
- Terminology and Symbols
- Chapter 6. Trig Identities to Logarithms
- Law of Sines
- Law of Cosines
- Special Triangles
- Cofunctions
- Squared Functions
- Sums of Angles and Double Angles
- Prosthaphaeresis
- Turning Multiplication into Addition
- Logarithms
- Slide Rules
- Powers and Roots
- Make a Slide Rule
- Paper Slide Rule
- Logs for Estimation
- Chapter Key Points
- Terminology and Symbols
- References
- Chapter 7. Navigation
- Measuring Angles and Distances
- Inclinometer
- Finding Latitude
- Polaris
- Southern Skies
- Sailing Down the Latitude
- Astrolabe
- Sextant
- Navigational Uses
- Measuring Height with a Sextant
- GPS
- Chapter Key Points
- Terminology and Symbols
- References
- Chapter 8. Making Waves
- Adding Waves
- Constructive and Destructive Interference
- Propagation in Space and Time
- Wave Interference Model
- Electromagnetic Waves
- Refraction
- Rotated Coordinate Systems
- Snell's Law
- Lenses
- Reflection
- Stokes' Relations
- Water and Sound Waves
- Modeling a Helicoid
- Chapter Key Points
- Terminology and Symbols
- References
- Chapter 9. Ellipses and Circles
- Conic Sections
- Anatomy of a Cone
- Conics Overview Model
- Circle Cross-section
- Ellipse Cross-section
- Parabola Cross-section
- Hyperbola Cross-section
- Cutting a Play-Doh Cone
- Conic Sections and Angles
- Ellipses and Circles
- Eccentricity
- Finding the Foci
- Equation of a Circle and an Ellipse
- Translating Circles and Ellipses
- Equations of Rotated Circles and Ellipses
- Area of an Ellipse
- Circumference of a Circle and an Ellipse
- Ellipses in the Wild
- Terminology and Symbols
- Chapter Key Points
- References
- Chapter 10. Parabolas and the Quadratic Formula
- Parabolas
- Focus and Directrix
- Drawing a Parabola
- The Parabola Model
- Assembling the Model
- Learning with the Model
- Equation of a Parabola
- Translating the Parabola
- Quadratic Equations
- Roots: The Fundamental Theorem of Algebra
- Completing the Square
- The Quadratic Formula
- Focus, Directrix and Vertex
- Changing the Curve
- Parabolas in the Wild
- Parabolic Mirrors
- Galileo Ramp
- Finding a Maximum or Minimum
- Terminology and Symbols
- Chapter Key Points
- References
- Chapter 11. Hyperbolas
- Hyperbola Conic Section
- Graphing a Hyperbola
- Foci and Directrix
- The Hyperbola Model
- Do Not Shrink This Model
- Assembling the Model
- Learning with the Model
- Model Limitations
- Equation of a Hyperbola
- Asymptotes
- Another Example
- Reciprocal Form
- Hyperbolic Mirrors
- Hyperbolic Trigonometry
- Terminology and Symbols
- Chapter Key Points
- References
- Chapter 12. Applications and Looking Ahead
- Tilings
- Tilings with Regular Polygons
- Aperiodic Tilings
- Robot Control
- Building the Robot Arm
- Wiring the Arm
- Programming the Arm
- Analyzing the Arm Motion
- Converting Cartesian to Spherical Coordinates
- The atan2 Function
- Walkthrough of the Arduino Code
- Running the Robot
- Building on this Project
- Looking Forward to Calculus
- Chapter Key Points
- Terminology and Symbols
- Resources
- Sources for this Chapter
- Websites and Search Terms
- Calculation Resources
- Books
- Appendix A. Topics Covered
- Index
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