Trigonometry

The Rotating WheelINTRO

Building the Unit CircleINTRO

Shaded Regions on the Unit CircleINTRO

Unwrapping the CircleINTRO

Degrees and RadiansLESSON

Converting Between Degrees and RadiansEXAMPLE

Angle ConverterLESSON

Coterminal AnglesLESSON

Finding Coterminal AnglesPRACTICE

The Unit Circle ClockLESSON

Memorizing the Unit CircleEXAMPLE

Defining Sine and CosineLESSON

Right Triangle DefinitionsLESSON

Sine and Cosine CalculatorLESSON

Evaluating sin(π/3) and cos(5π/4)EXAMPLE

Angles in Four QuadrantsLESSON

Finding Reference AnglesEXAMPLE

Reference Angle ApplicationsPRACTICE

Reciprocal and Quotient IdentitiesLESSON

Pythagorean IdentitiesLESSON

Sum and Difference FormulasLESSON

Solving sin(x) = 1/2LESSON

Solving cos(x) ≤ 1/2LESSON

Inequality GrapherLESSON

Solving sin(x) + sin(y) = 1 and cos(x) + cos(y) = 1EXAMPLE

Inverse Function ExplorerLESSON

27

Roots of UnityLESSON

28

Arc Length in PolarLESSON

29

Calculus Connection ExplorerLESSON

30

Foundations SummaryLESSON

31

Master Trigonometry ReferenceFORMULA SHEET

2

Right Triangle Trigonometry

Master right triangle trigonometry

13 modules

SOH-CAH-TOA RevivalINTRO

Beyond Right TrianglesINTRO

Triangle SolverLESSON

Finding Missing SidesEXAMPLE

Evaluating sin(arccos(3/5))EXAMPLE

Angle of Elevation ProblemsLESSON

Right Triangle ApplicationsPRACTICE

Deriving the Law of SinesLESSON

Triangle Solver - Law of SinesLESSON

Ambiguous Case (SSA)LESSON

Triangle Solver - Law of CosinesLESSON

Applications SummaryLESSON

Trigonometric Functions ReferenceFORMULA SHEET

3

Trigonometric Functions

Master trigonometric functions

30 modules

Beyond Sine and CosineINTRO

Path of a Bicycle WheelINTRO

Beyond Base Times HeightINTRO

Special Angles and Their CoordinatesLESSON

Special Angle ValuesPRACTICE

Defining Four More FunctionsLESSON

Six Function EvaluatorLESSON

Calculating tan(7π/6) and sec(-π/4)EXAMPLE

Trigonometric Function ValuesPRACTICE

Sign Patterns in QuadrantsLESSON

Quadrant DetectiveLESSON

Angle CalculatorLESSON

Finding arccos(-√3/2)EXAMPLE

Converting (-2, 2√3) to PolarEXAMPLE

Converting (3, π/6) to RectangularEXAMPLE

Height on a Ferris WheelLESSON

Shadow Length CalculatorLESSON

Finding All Solutions to cos(x) = -√2/2EXAMPLE

Double-Angle FormulasLESSON

Finding cos(2θ) When sin(θ) = 3/5EXAMPLE

Half-Angle ExplorerLESSON

Sum-to-Product FormulasLESSON

Finding sin(75°) ExactlyEXAMPLE

Difference Formula ApplicationsPRACTICE

Formula ConverterLESSON

Finding Area with Two Sides and Included AngleEXAMPLE

Area CalculatorLESSON

27

28

Finding the Third Side (SAS)EXAMPLE

29

Area Calculation PracticePRACTICE

30

Land SurveyingLESSON

4

Graphs of Trig Functions

Master graphs of trig functions

41 modules

Drawing with AnglesINTRO

Building Waves from SinesINTRO

Compressed WavesINTRO

When Waves CrossINTRO

The Tangent CurveINTRO

Shifting and Stretching WavesINTRO

The Basic Sine and Cosine CurvesLESSON

Graphing y = sin(x) from 0 to 4πEXAMPLE

Sine and Cosine GraphsPRACTICE

Wave CharacteristicsLESSON

General Form y = A sin(B(x - C)) + DLESSON

Graphing y = 3sin(2x - π/2) + 1EXAMPLE

Transformation LaboratoryLESSON

Wave GeneratorLESSON

Writing Equations from GraphsPRACTICE

Graphing Tangent, Cotangent, Secant, and CosecantLESSON

Graphing y = tan(x - π/4)EXAMPLE

Reciprocal Function GrapherLESSON

Asymptote ExplorerLESSON

Other Function GraphsPRACTICE

Product-to-Sum FormulasLESSON

Defining Arcsin, Arccos, and ArctanLESSON

Inverse Function MethodLESSON

Solving cos(x/2) = -1/2EXAMPLE

Equation Solver VisualizerLESSON

Solving Equations SummaryLESSON

27

Graphing x = 2cos(t), y = 3sin(t)EXAMPLE

28

Graphing r = 2 + 2cos(θ)EXAMPLE

29

Polar Graphing PracticePRACTICE

30

Harmonic AnalysisLESSON

31

Fourier Coefficient CalculatorLESSON

32

Fourier ConceptsPRACTICE

33

Wave Interference SimulatorLESSON

34

Sound Wave ModelerLESSON

35

CrystallographyLESSON

36

Vector Addition ToolLESSON

37

Vectors SummaryLESSON

38

Trigonometry in Your WorldLESSON

39

Graphing SummaryLESSON

40

Graphing ReferenceFORMULA SHEET

41

Comprehensive Final ExamQUIZ

5

Trigonometric Identities

Master trigonometric identities

22 modules

6

Sum, Difference, and Multiple Angle Formulas

Master sum, difference, and multiple angle formulas

1 modules

Angle Addition DiscoveryINTRO

7

Inverse Trigonometric Functions

Master inverse trigonometric functions

17 modules

Undoing TrigonometryINTRO

Reversing the ProcessINTRO

Why Restrict the Domain?LESSON

Cancellation PropertiesLESSON

Composition CalculatorLESSON

Basic Inverse EvaluationPRACTICE

Equation Strategy GuideLESSON

Solving arctan(x) + arctan(2x) = π/4EXAMPLE

Solving sin(2x - π/3) = 1/2EXAMPLE

Mixed Equation PracticePRACTICE

Inverse Function ModelerLESSON

Angle of ViewLESSON

Engineering TolerancesEXAMPLE

Converting 3 + 4i to Polar FormEXAMPLE

Application ProblemsPRACTICE

Inverse Functions SummaryLESSON

Inverse Functions ReferenceFORMULA SHEET

8

Solving Trigonometric Equations

Master solving trigonometric equations

26 modules

System of Trigonometric EquationsINTRO

Advanced Equation SolverLESSON

Solving 2sin(x) - 1 > 0EXAMPLE

Solving tan(x) + cot(x) = 2EXAMPLE

Solving 2cos²(x) - cos(x) - 1 = 0EXAMPLE

Basic Equation PracticePRACTICE

Frequency AnalyzerLESSON

Solving sin(3x) = √3/2EXAMPLE

Multiple-Angle EquationsPRACTICE

Multiple-Angle PracticePRACTICE

Inequality ApplicationsPRACTICE

Functions SummaryLESSON

Identities SummaryLESSON

Problem-Solving MasterclassLESSON

Defining Parametric EquationsLESSON

Parametric Trigonometric EquationsLESSON

Common Polar CurvesLESSON

Polar Art StudioLESSON

Solving Triangle with A = 40°, B = 60°, c = 10EXAMPLE

Law of Sines PracticePRACTICE

3D Trigonometry LabLESSON

Wind and AirspeedLESSON

Finding Angle Between VectorsEXAMPLE

Vector Problem SolvingPRACTICE

Challenge Problem SetPRACTICE

Equation-Solving ReferenceFORMULA SHEET

9

Law of Sines and Cosines

Master law of sines and cosines

7 modules

The Missing PieceINTRO

Area Formulas Using TrigonometryLESSON

Heron's Formula ApplicationEXAMPLE

Finding Angles from Three Sides (SSS)EXAMPLE

Law of Cosines PracticePRACTICE

Navigation ProblemLESSON

Applications ReferenceFORMULA SHEET

10

Vectors

Master vectors

22 modules

11

Polar Coordinates and Complex Numbers

Master polar coordinates and complex numbers

16 modules

Rates of ChangeINTRO

Radar Screen NavigationINTRO

Complex Plane NavigationINTRO

Defining Polar CoordinatesLESSON

Coordinate ConverterLESSON

Polar-Rectangular PracticePRACTICE

Rose Curves r = a sin(nθ)LESSON

Area Inside Polar CurvesLESSON

Polar Form of Complex NumbersLESSON

Complex Number CalculatorLESSON

Complex Number PracticePRACTICE

DeMoivre's TheoremLESSON

Finding (1 + i)^8EXAMPLE

Analytic Trigonometry SummaryLESSON

Alternative Coordinates SummaryLESSON

Polar and Parametric ReferenceFORMULA SHEET

12

Parametric Equations

Master parametric equations

3 modules

Parametric Curve TracerLESSON

Tide PredictorLESSON

Converting Between FormsPRACTICE

13

Applications and Course Conclusion

Master applications and course conclusion

12 modules

Navigation in SpaceINTRO

Doubling and HalvingINTRO

Historical JourneyLESSON

Connections WebLESSON

Projectile PathLESSON

Finding Angles in PhysicsLESSON

Music SynthesizerLESSON

Distance Between CitiesLESSON

Power-Reducing FormulasLESSON

Converting 2sin(3x)cos(x) to SumEXAMPLE

Advanced ApplicationsPRACTICE