book

Make: Trigonometry

by Joan Horvath, Rich Cameron

August 2023

Beginner to intermediate

354 pages

8h 27m

English

Make: Community

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Who This Book Is ForTeaching and Learning with This BookWhat You Will NeedAcknowledgmentsAbout the Authors
TrigonometryAnalytic GeometryStructure of This BookMath Concepts to KnowChapter Key Points
OpenSCADOpenSCAD WorkflowNavigating on the ScreenCommentsIdiosyncrasies of OpenSCADThe ModelsExample 1: Changing a ParameterExample 2: Changing a Model with the CustomizerDownloading the Models: GithubSome Models Have Small Parts3D Printing3D Printing WorkflowMaterialsPrinting TipsIf You Do Not Have a 3D PrinterChapter Key PointsTerminology and SymbolsReferences
Angles of a TriangleDegrees, Radians, and PiProve Triangle Angles Add to 180°How to Use a ProtractorDrawing and Labeling TrianglesCongruent TrianglesSimilar TrianglesTrigonometry BasicsPythagorean TheoremSquares and Square RootsPythagoras’ LEGO BricksSine, Cosine, TangentHypotenuse ModelComplementary AnglesOther RatiosAngles Greater Than 90°Finding the Length of a SideArcsin, Arccos, ArctanCalculating with Sine and CosineMeasure Something BigTesting with a Known ObjectGarage Roof HeightChapter Key PointsTerminology and SymbolsReferencesAnswersHypotenuse ModelCalculating with Sine and Cosine
Analytic GeometryCoordinate SystemsCoordinate System ModelModel ParametersCartesian CoordinatesGraphing a Line3D CoordinatesPolar CoordinatesCylindrical CoordinatesSpherical CoordinatesMaking Curves and SurfacesCraft Materials Models3D Printed ModelsChapter Key PointsTerminology and Symbols
Beyond the Right TriangleAngles Between 90° and 180°Angles Between 180° and 270°Angles Between 270° and 360° (or -90° and 0°)Principal ValueThe Unit CircleMaking 3D Printed ModelsSine Versus CosineRolling Out a Sine CurvePhaseFrequencyAmplitudeAngular FrequencyPeriodPaper ModelsGraphing Trig FunctionsGraphing Sinusoids in Cartesian CoordinatesPolar Graphs of SinusoidsGraphing in RadiansChapter Key PointsTerminology and Symbols
Law of SinesLaw of CosinesSpecial TrianglesCofunctionsSquared FunctionsSums of Angles and Double AnglesProsthaphaeresisTurning Multiplication into AdditionLogarithmsSlide RulesPowers and RootsMake a Slide RulePaper Slide RuleLogs for EstimationChapter Key PointsTerminology and SymbolsReferences
Measuring Angles and DistancesInclinometerFinding LatitudePolarisSouthern SkiesSailing Down the LatitudeAstrolabeSextantNavigational UsesMeasuring Height with a SextantGPSChapter Key PointsTerminology and SymbolsReferences
Adding WavesConstructive and Destructive InterferencePropagation in Space and TimeWave Interference ModelElectromagnetic WavesRefractionRotated Coordinate SystemsSnell’s LawLensesReflectionStokes’ RelationsWater and Sound WavesModeling a HelicoidChapter Key PointsTerminology and SymbolsReferences
Conic SectionsAnatomy of a ConeConics Overview ModelCircle Cross-sectionEllipse Cross-sectionParabola Cross-sectionHyperbola Cross-sectionCutting a Play-Doh ConeConic Sections and AnglesEllipses and CirclesEccentricityFinding the FociEquation of a Circle and an EllipseTranslating Circles and EllipsesEquations of Rotated Circles and EllipsesArea of an EllipseCircumference of a Circle and an EllipseEllipses in the WildTerminology and SymbolsChapter Key PointsReferences

ParabolasFocus and DirectrixDrawing a ParabolaThe Parabola ModelAssembling the ModelLearning with the ModelEquation of a ParabolaTranslating the ParabolaQuadratic EquationsRoots: The Fundamental Theorem of AlgebraCompleting the SquareThe Quadratic FormulaFocus, Directrix and VertexChanging the CurveParabolas in the WildParabolic MirrorsGalileo RampFinding a Maximum or MinimumTerminology and SymbolsChapter Key PointsReferences
Hyperbola Conic SectionGraphing a HyperbolaFoci and DirectrixThe Hyperbola ModelDo Not Shrink This ModelAssembling the ModelLearning with the ModelModel LimitationsEquation of a HyperbolaAsymptotesAnother ExampleReciprocal FormHyperbolic MirrorsHyperbolic TrigonometryTerminology and SymbolsChapter Key PointsReferences
TilingsTilings with Regular PolygonsAperiodic TilingsRobot ControlBuilding the Robot ArmWiring the ArmProgramming the ArmAnalyzing the Arm MotionConverting Cartesian to Spherical CoordinatesThe atan2 FunctionWalkthrough of the Arduino CodeRunning the RobotBuilding on this ProjectLooking Forward to CalculusChapter Key PointsTerminology and SymbolsResourcesSources for this ChapterWebsites and Search TermsCalculation ResourcesBooks

Content preview from Make: Trigonometry

Chapter 4. Coordinate Systems and Analytic Geometry

One of the most familiar things in any math textbook is a grid with arrows marking the direction of increasing x, y, or some other variable. We saw three-dimensional examples in Chapter 2 when we introduced OpenSCAD. ...

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Publisher Resources

ISBN: 9781680458183Errata Page