Outline
Trigonometry
Table of Contents
Prerequisites
- Perpendicular Lines: Quick Intro
- Complementary Meaning?
- Supplementary Angles (Quick Exploration)
- Isosceles Triangle (Quick Construction Technique) V1
- Equilateral Triangle Construction (Dynamic Illustration)
- Proof Without Words
- Proof Without Words
- Practice: Pythagorean Theorem (1)
- Quiz: Pythagorean Theorem (2A)
- Quiz: Pythagorean Theorem (2B)
- Simplifying Radicals (I)
- Simplifying Radicals (II)
- Triangle Angle Sum Theorem (V4)
- Animation 171
- Isosceles Right Triangle: Quick Investigation
- Another Special Right Triangle (Guided Discovery)
- Special Right Triangle (II)
- Vertical Angles Exploration (1)
- Naming Angle Positions
- Transversal Intersects Parallel Lines
- Corresponding Angles: Quick Investigation
- Alternate Interior Angles: Quick Investigation
- Alternate Exterior Angles: Quick Investigation
- Same-Side-Interior Angles: Quick Investigation
- Same-Side-Exterior Angles: Quick Investigation
- Similar Figures: Dynamic Illustration
- AA Similarity Theorem
- SSS ~ Theorem (V2)
Standard Position & Vocab
6 Trig Functions; Quadrant Logic
- The 6 Trigonometric Functions: Quick Illustrator
- Quiz: Evaluating Trigonometric Functions of Angles Given a Point on its Terminal Ray
- Evaluating Trig Functions Given a Point on the Terminal Ray
- Quiz: Quadrant Logic (Trig)
- Trig Quadrant Logic (2)
- Trig Ratio Possibilities (Hints)
- Quiz: Evaluating Trig FNS of Angles (Quadrant Logic): V1
- Quiz: Evaluating Trig FNS of Angles WITH Quadrant Logic (V2)
Right Triangle Trig (Q1)
- Right Triangle Generator for Right Triangle Trigonometry
- Right Triangles: Identifying Sides WRT Acute Angles
- Identifying Trig Ratios: Quick Formative Assessment
- Finding Exact Trig Ratios: Quiz Question Generator
- Right Triangle Trigonometry: Intro
- True Meaning of Sine, Cosine, Tangent Ratios within Right Triangles
- Trig Ratio Estimations (Right Triangle Context)
- Trig Ratio Estimations (Quiz: V1)
- Right Triangle Solver: Formative Assessment
- Right Triangle Trig: Solving for Sides
- Right Triangle Trig: Solving for Sides (2)
- Using Inverse Trig Functions to Find Acute Angles of Right Triangles
- Quiz: Expressing Angles Using Inverse Trigonometric Function
- What "CO" in COsine Means
Radians, Arc Length, Sector Area
- What is a Radian?
- Radian Illustrator
- 1 Radian: Clear Definition
- Constructing Angles Given Radian Measure
- Quiz: Sketching Angles in Standard Position
- TRUE MEANING of π
- Circumference = ? (Animation)
- Circumference = ? (Animation II)
- DEG to RAD and RAD to DEG Illustrator
- DEG to RAD and RAD to DEG: Question Generator
- Arc length: Quick Investigation
- Parallelogram: Area
- Triangle Area Action!!! (V2)
- Circle Area (By Peeling!)
- Arc Length and Area of a Sector (V1)
- Arc Length and Area of a Sector (V2)
- Area of a Sector
- Angular to Linear: Without Words
- YOUR Linear Speed?
- Who's Going Faster?
Trig FNS of Special Angles
- Trig Function Values (30 Degrees)
- Trig Function Values (45 Degrees)
- Trig Function Values (60 Degrees)
- Special Right Triangles: Basic Questions
- Quiz: Special Right Triangles
- Trig Reference Circle: Choose Your Own Radius
- Trig Reference Circle (2): Choose Your Own Radius
- Rads and Revs: Quick Conceptual Insight
- Trig Circle: Coordinates of Special Angle Values
- Special Angles in Standard Position: Intro (V2)
- Special Angles in Standard Position: Intro (V3)
- Quiz 1: Trigonometric Functions of Special Angles
- Quiz 2: Trigonometric Functions of Special Angles
Graphing and Writing Trig Functions & Equations
- Parent Sine and Cosine Functions
- Sine and Cosine Graphing Template
- Sine and Cosine π-friendly Graphing Template
- Sine Spaghetti (by Steve Phelps)
- Cosine Spaghetti
- Sine Function Anatomy and Exploration
- Unit Circle to Sine and Cosine Functions
- Tangent Function Exploration
- Cotangent Function Exploration
- Transforming Sine and Cosine Functions (1): Dynamic Illustrator
- Transforming Sine and Cosine Functions (2): Dynamic Illustrator
- Sine & Cosine Period Action (1)!
- Periodic Function Action!
- Quiz: Graphing Sine & Cosine Functions (Amplitude & Vertical Shift Only)
- Writing Sine and Cosine Functions (with Amplitude & Vertical Shift Changes)
- Basic Trig Graphing Open Middle Problem
- Open Middle: Graphing Trig Functions Exercise
- Graphing Sine & Cosine Functions (Amp, Period, Vertical Shift Changes Only)
- Graphing Sine and Cosine Functions (Includes All Transformations)
- Modeling with Trigonometric Functions
- Open Middle: Trigonometric Equation (1)
- Open Middle: Trigonometric Equation (2)
- Open Middle: Creating Trig EQ's Exercise Set
- Transforming the Sine Function (All Transformations)
- Graphing Sine & Cosine Functions (I)
- Graphing Sine & Cosine Functions (II)
Inverse Trig Functions
- Using Inverse Trig Functions to Express Angle Measures
- Creating Inverse Sine and Inverse Cosine Functions
- Inverse Trig Functions: Intuitive Explorations
- Evaluating Inverse Trig Functions of Special Ratios
- Compositions of Trig & Inverse Trig Functions (1)
- Evaluating Compositions of Trig & Inverse Trig Functions (2)
Proving Trig ID's
- New Trig IDs From Similar Right Triangles
- New Trig ID's from Similar Right Triangles (V2)
- Another Popular Trig Identity
- Trig Identity via Areas: Dynamic Illustrator
- Trig Identity via Areas (2): Dynamic Illustrator
- Sine & Cosine of a Sum: Discovery
- Tangent of a Sum: Discovery
- Cotangent of a Sum: Discovery
- Trig ID: Geometric Investigation
- Trig ID (2) - Geometric Investigation
- Trig Identity (3) - Geometric Investigation
- Trig Identity (4) - Geometric Investigation
- Double Angle Trig Identity: Proof via Equal Areas
- Trig Identity Shown Graphically
Advanced Topics
- Special Trigonometric Identities: Quick Exploration
- Exploring Sines: Another Key Triangle Relationship
- Law of Sines: Intro via Areas
- Law of Sines (& Area)
- Interesting Triangles Phenomenon
- SSA Theorem?
- Ambiguous Case (SSA) Illustrator: All Cases
- Open Middle: Ambiguous Case Setups
- Law of Cosines: Discovery
- Law of Cosines: Open Middle Problem (V1)
- Open Middle Problem: Law of Cosines (V2)
Bearings (Applications)
Vectors
- Vectors: Magnitude & Direction (I)
- Scaling Vectors
- Vector Addition
- Quiz: Adding Vectors Geometrically
- Vector Subtraction
- Dot Product Insight
- Orthogonality Illustrated
- Dot Product: Basic Synthesis Questions
- Vector Projections (1)
- Quality Info?
- Vector Magnitude from Components
- Magnitude and Direction (Intro)
- Pac Man: Vector Components
Dot Product
- Mystery Scalar Exploration (Part 1)
- Mystery Scalar Exploration (Part 1)
- Mystery Scalar Exploration (Part 3)
- Mystery Scalar Exploration (Part 4)
- Mystery Scalar Exploration (Part 5)
- Mystery Scalar Exploration (Part 6)
- Mystery Scalar Exploration (Part 7)
- Mystery Scalar Exploration (Part 8)
- Mystery Scalar Exploration (Part 9)