Trigonometry

Table of Contents

• Unit Circle/ Laws

  • The Unit Circle
  • Unit Circle - Identifying Coordinates for Important Angles
  • Unit Circle
  • Unwrapping a Circle
  • Unwrapping the Unit Circle
  • Sine an Cosine Components
  • law of cosines (proof)
  • law of sines (proof)
  • Law of sines-ambiguous case

• Preliminary Content

  • 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)

• Angles in Standard Position (and Related Vocabulary)

  • Angles in Standard Position
  • Angle Orientations (Standard Position)
  • Coterminal Angles Action!!!

• The 6 Trigonometric Ratios; Right Triangle Trigonometry; Applications

  • Right Triangles: Identifying Sides WRT Acute Angles
  • Identifying Trig Ratios: Quick Formative Assessment
  • Finding Exact Trig Ratios: Quiz Question Generator
  • 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 Generator for Right Triangle Trigonometry
  • 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)
  • Finding Acute Angles of Right Triangles
  • Quiz: Expressing Angles Using Inverse Trigonometric Function
  • What "CO" in COsine Means

• Trigonometric Functions 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
  • 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

• Introduction to Radians; Arc Length and Area of a Sector

  • Circle vs. Sphere
  • Circle Terminology
  • TRUE MEANING of π
  • Circumference = ? (Animation)
  • Circumference = ? (Animation II)
  • 1 Radian: Clear Definition
  • Radian Illustrator
  • Quiz: Sketching Angles in Standard Position
  • 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?

• Graphing and Writing Trigonometric Functions

  • 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
  • Quiz: Graphing Sine & Cosine Functions (Amplitude & Vertical Shift Only)
  • Writing Sine and Cosine Functions (with Amplitude & Vertical Shift Changes)
  • Periodic Function Action!
  • Transforming the Sine Function (All Transformations)
  • Sine & Cosine Period Action (1)!
  • Graphing Sine & Cosine Functions (I)
  • Graphing Sine & Cosine Functions (II)
  • Modeling with Trigonometric Functions
  • Inverse Trig Functions: Intuitive Explorations

• Proving Trig Identities

  • New Trig IDs From Similar Right Triangles
  • New Trig ID's from Similar Right Triangles (V2)
  • Trig Identity via Areas: Dynamic Illustrator
  • Trig Identity via Areas (2): Dynamic Illustrator
  • Trig ID: Geometric Investigation

• Advanced Topics

  • Special Trigonometric Identities: Quick Exploration
  • Law of Sines (& Area)
  • SSA Theorem?
  • Ambiguous Case (SSA) Illustrator: All Cases
  • Law of Cosines: Discovery
  • Law of Cosines: Open Middle Problem (V1)
  • Open Middle Problem: Law of Cosines (V2)

• Bearings (Applications)

  • Bearing Illustrator (1)
  • Bearing: Dynamic Illustration
  • Bearing Illustrator (2)
  • Bearings: Dynamic Illustrator

• 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 Discovery Lesson

  • 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)