内容目录

1. Pythagoras Theorem 14
   1. A way to find the value of a square root?
2. Basic Graphing
   1. Basic Trig -360 x 360
   2. Basic Trig Graph -2π x 2π by -10 x 10
   3. Degree Trig Chart Creator
   4. Sine Curve with Abscissa in Degrees
   5. The General Cosine Function
   6. Trace the Sine or Cosine Functions
   7. Trace the Tangent or Cotangent Functions
   8. sun(x): a trigonometric function
3. Degrees-Radian Measures
   1. Degrees vs Radians
   2. Radian Units
   3. Basic Trig -360° x 360°
   4. Full Circle Protractors
4. Unit Circle
   1. Unit Circle
   2. Unit CircleTriangles
   3. Unit Circle Triangles
   4. What class of Triangles use Pythagorean Theorem?
5. Sample Problems
   1. Find distance between Cities
   2. Find the height
   3. Raise the Flag
   4. Find Building Height
   5. Example of Snell's Law of Refraction
6. Definitions of Trigonometry
   1. Basic Terms in Geometry
   2. The terms Adjacent, Hypotenuse, and Opposite sides
   3. Mnemonic for Learning Trig Function Values in Quadrant I
   4. The Standard Position of an Angle
   5. Standard Position (Improved)
   6. Defining the Coterminal Angle
   7. Reference Angles
   8. Trigonometry Terms
   9. Dividing Trigonometric Functions
   10. Finding an Inverse for the Cosine Function
   11. Finding an Inverse for the Tangent Function
   12. Triangle Inequality
   13. Triangle Inequality
   14. Trig Value Chart by 15°
   15. Trig Value Chart by π/12
7. Functions
   1. 1st Definition of Trigonometry Functions
   2. 2nd Definition of Trigonometry Functions (SohCahToa)
   3. SohCahToa
   4. Projection of Radius on x-Axis and y-Axis
   5. Function Review of Trigonometry
   6. Addition of 2 Sine Functions
   7. Adding 2 Sine Functions Graphically
   8. Adding Trigonometric Functions
   9. Subtracting Trigonometric Functions
   10. Multiplying Trigonometric Functions
   11. Composition of Trigonometric Functions
   12. The General Secant Function
   13. The General Sine Function
   14. Transform Sine/Cosecant
   15. Transform Cosine/Secant
   16. Transform Tangent/Cotangent
   17. Phase Shift of Trig Functions {tan(x) or cot(x)}
   18. Phase Shift of Trig Funct {sin(x), cos(x), sec(x), csc(x)}
   19. The Period of Trig Functs {tan(x) or cot(x)}
   20. The Period Trig Functions sin(x), cos(x), sec(x), or csc(x)
   21. Polar graph with rectangular graph
   22. Morphing Cartesian Graphs to Polar Graphs
8. Identities
   1. Trigonometric Identity Explorer
   2. Circle of Symmetry Sine/Cosine
   3. Developing the Law of the Sine
   4. Relate Sin(a + b) and Sin(a-b)
   5. Law of Sines
   6. Developing the Law of Cosines
   7. Exploring the Ambiguous Case of the Law of Sines
   8. Trig Unspecified Triangle Cos Law
   9. Law of Sines
   10. The Sine Law
9. Geometry
   1. Full Circle Protractors
   2. Intersecting Line Properties
   3. Parallel Line Theorems
   4. Triangle: Sum of Interior Angles
   5. Finding sums of angles
   6. Parallel & Perpendicular Linear Equations
   7. What class of Triangles use Pythagorean Theorem?
   8. Triangle Inequality
   9. Triangle Inequality
   10. Triangle: Sum of Remote Interior Angles & Exterior Angle
   11. Triangle: Proportionality
   12. Quadrilateral Tools
   13. Diagonal Hint for a Rectangular Prism
   14. Pythagorean Theorem (Converse)
   15. Polygon Proofs of Pythagoras
   16. All Poly Proof of Pythagoras
   17. Pythagorean Proof SemiCircle
   18. Three-Dimensional Pythagorean Theorem
   19. Triangle Centers
   20. TRUE MEANING of π
   21. Classify Triangles by Angle
   22. Supplementary Angles Meaning
   23. Complementary Angles Meaning
   24. PolygonTypes
   25. Area of Regular Polygon
   26. Regular Polygons (with Limits)
10. HSF.TF.A.1: Working with radians
    1. 1 Radian: Clear Definition
    2. Animation 69
    3. Radian Illustrator
    4. Movie: Radians to Revs
    5. DEG to RAD and RAD to DEG Illustrator
    6. DEG to RAD and RAD to DEG: Question Generator
11. HSF.TF.A.2: Angles in standard position, coterminal angles, trigonometric ratios
    1. Angles in Standard Position
    2. Animation 176
    3. Angle Orientations (Standard Position)
    4. Animation 180
    5. Animation 181
    6. Coterminal Angles Action!!!
    7. Animation 183
    8. Quiz: Sketching Angles in Standard Position
    9. Coterminal Angles: Question Generator
    10. Defining Trigonometric Ratios
    11. Unit Circle and Sine Graph
    12. Unit Circle and Tangent Graph
    13. Unit Circle and Cosine Graph
12. HSF.TF.A.3: Trigonometric functions of special angles (multiples of pi/6 & pi/4)
    1. Right Triangle Generator for Right Triangle Trigonometry
    2. Quiz: Evaluating Trigonometric Functions of Angles Given a Point on its Terminal Ray
    3. Evaluating Trig Functions Given a Point on the Terminal Ray
    4. Quiz: Quadrant Logic (Trig)
    5. Trig Quadrant Logic (2)
    6. Quiz: Evaluating Trig FNS of Angles (Quadrant Logic): V1
    7. Quiz: Evaluating Trig FNS of Angles WITH Quadrant Logic (V2)
    8. Right Triangle Trigonometry: Intro
    9. True Meaning of Sine, Cosine, Tangent Ratios within Right Triangles
    10. Right Triangle Solver: Formative Assessment
    11. Right Triangle Trig: Solving for Sides (2)
    12. Quiz: Expressing Angles Using Inverse Trigonometric Function
    13. Trig Ratio Estimations (Right Triangle Context)
    14. Trig Ratio Estimations (Quiz: V1)
    15. Trig Ratio Estimations (Quiz: V2)
    16. Isosceles Right Triangle: Quick Investigation
    17. Special Right Triangle (I)
    18. Another Special Right Triangle (Guided Discovery)
    19. Special Right Triangle (II)
    20. 30-60-90 Triangle
    21. Special Right Triangles: Basic Questions
    22. Quiz: Special Right Triangles
    23. Trig Function Values (30 Degrees)
    24. Animation 148
    25. Trig Function Values (45 Degrees)
    26. Animation 146
    27. Trig Function Values (60 Degrees)
    28. Animation 147
    29. Special Angles in Standard Position: Intro (V1)
    30. Special Angles in Standard Position: Intro (V2)
    31. Special Angles in Standard Position: Intro (V2) - Part 2
    32. Animation 177
    33. Animation 178
    34. Special Angles in Standard Position: Intro (V3)
    35. Animation 182
    36. Quiz 1: Trigonometric Functions of Special Angles
    37. Quiz 2: Trigonometric Functions of Special Angles
13. HSF.TF.A.4: Which trig functions are even? odd?
    1. Sine and Cosecant Functions (Special Property)
    2. Sine Identity
    3. Animation 150
    4. Cosine and Secant Functions (Special Property)
    5. Cosine Identity
    6. Animation 149
    7. Tangent and Cotangent Functions (Special Property)
    8. Animation 145
    9. Tangent Identity
    10. Animation 151
14. HSF.TF.B.5: Graphing and writing trigonometric functions
    1. Unit Circle to Sine and Cosine Functions
    2. Sine & Cosine Period Action (1)!
    3. Animation 190
    4. Animation 191
    5. Sine & Cosine Period Action (2)!
    6. Tangent Function Exploration
    7. Tangent Period Action (1)!
    8. Tangent Period Action (2)!
    9. Animation 192
    10. Cotangent Function Exploration
    11. Transforming Sine and Cosine Functions (1): Dynamic Illustrator
    12. Transforming Sine and Cosine Functions (2): Dynamic Illustrator
    13. Transforming the Sine Function (All Transformations)
    14. Graphing Sine & Cosine Functions (II)
    15. Graphing Sine & Cosine Functions (I)
    16. Transformations of a Sinusoid
    17. Quiz: Graphing Sine & Cosine Functions (Amplitude & Vertical Shift Only)
    18. Writing Sine and Cosine Functions (with Amplitude & Vertical Shift Changes)
    19. Sine Function Modeling (y = a sin(x) + d) Quiz
    20. Cosine Function Modeling (y = a cos(x) + d) Quiz
    21. Modeling with Trigonometric Functions
    22. Sine & Cosine Function Modeling: Finding Correct Parameters
    23. Ferris Wheel Action!!!
15. HSF.TF.B.6: Inverse trigonometric functions
    1. Inverse Relations: Graphs
    2. Sine Function Domain Restriction Options?
    3. Cosine Function Domain Restriction Options?
    4. Tangent Function Domain Restriction Options?
    5. Inverse Trig Functions: Intuitive Explorations
16. HSF.TF.B.7: Solving trigonometric equations and modeling
    1. Ferris Wheel (1): Modeling with Trigonometric Functions
    2. Ferris Wheel (2): Modeling with Trigonometric Functions
17. HSF.TF.C.8: Proving trigonometric identities
    1. New Trig IDs From Similar Right Triangles
    2. New Trig ID's from Similar Right Triangles (V2)
    3. Pythagorean Trigonometric Identity (1)
    4. Trig ID Movie (II)
    5. Trig ID Movie (III)
18. HSF.TF.C.9: Proving advanced trigonometric identities
    1. Sine & Cosine of a Sum: Discovery
    2. Trig ID: Geometric Investigation
    3. Tangent of a Sum: Discovery
    4. Tangent of a Difference: Trig Identity Puzzle + Proof!
    5. Cotangent of a Sum: Discovery
    6. Bizzare Trig Identity?
    7. Animation 105
    8. sin(75) & cos(75) activity
19. Links to Other CCSS High School: Functions Resources
    1. Functions Resources
20. *Additional: Links to CCSS High School: Geometry Resources
    1. Geometry Resources
21. Preliminary Content
    1. Perpendicular Lines: Quick Intro
    2. Complementary Angles Meaning
    3. Supplementary Angles Meaning
    4. Isosceles Triangle (Quick Construction Technique) V1
    5. Equilateral Triangle Construction (Dynamic Illustration)
    6. Proof Without Words
    7. Proof Without Words
    8. Practice: Pythagorean Theorem (1)
    9. Quiz: Pythagorean Theorem (2A)
    10. Quiz: Pythagorean Theorem (2B)
    11. Simplifying Radicals (I)
    12. Simplifying Radicals (II)
    13. Triangle Angle Sum Theorem (V4)
    14. Animation 171
    15. Isosceles Right Triangle: Quick Investigation
    16. Another Special Right Triangle (Guided Discovery)
    17. Special Right Triangle (II)
    18. Vertical Angles Exploration (1)
    19. Naming Angle Positions
    20. Transversal Intersects Parallel Lines
    21. Corresponding Angles: Quick Investigation
    22. Alternate Interior Angles: Quick Investigation
    23. Alternate Exterior Angles: Quick Investigation
    24. Same-Side-Interior Angles: Quick Investigation
    25. Same-Side-Exterior Angles: Quick Investigation
    26. Similar Figures: Dynamic Illustration
    27. AA Similarity Theorem
    28. SSS ~ Theorem (V2)
22. Angles in Standard Position (and Related Vocabulary)
    1. Angles in Standard Position
    2. Angle Orientations (Standard Position)
    3. Coterminal Angles Action!!!
23. The 6 Trigonometric Ratios; Right Triangle Trigonometry; Applications
    1. Right Triangles: Identifying Sides WRT Acute Angles
    2. Identifying Trig Ratios: Quick Formative Assessment
    3. Finding Exact Trig Ratios: Quiz Question Generator
    4. Quiz: Evaluating Trigonometric Functions of Angles Given a Point on its Terminal Ray
    5. Evaluating Trig Functions Given a Point on the Terminal Ray
    6. Quiz: Quadrant Logic (Trig)
    7. Trig Quadrant Logic (2)
    8. Trig Ratio Possibilities (Hints)
    9. Quiz: Evaluating Trig FNS of Angles (Quadrant Logic): V1
    10. Quiz: Evaluating Trig FNS of Angles WITH Quadrant Logic (V2)
    11. Right Triangle Generator for Right Triangle Trigonometry
    12. Right Triangle Trigonometry: Intro
    13. True Meaning of Sine, Cosine, Tangent Ratios within Right Triangles
    14. Trig Ratio Estimations (Right Triangle Context)
    15. Trig Ratio Estimations (Quiz: V1)
    16. Right Triangle Solver: Formative Assessment
    17. Right Triangle Trig: Solving for Sides
    18. Right Triangle Trig: Solving for Sides (2)
    19. Using Inverse Trig Functions to Find Acute Angles of Right Triangles
    20. Quiz: Expressing Angles Using Inverse Trigonometric Function
    21. What "CO" in COsine Means
24. Trigonometric Functions of Special Angles
    1. Trig Function Values (30 Degrees)
    2. Trig Function Values (45 Degrees)
    3. Trig Function Values (60 Degrees)
    4. Special Right Triangles: Basic Questions
    5. Quiz: Special Right Triangles
    6. Special Angles in Standard Position: Intro (V2)
    7. Special Angles in Standard Position: Intro (V3)
    8. Quiz 1: Trigonometric Functions of Special Angles
    9. Quiz 2: Trigonometric Functions of Special Angles
25. Introduction to Radians; Arc Length and Area of a Sector
    1. Circle vs. Sphere
    2. Circle Terminology
    3. TRUE MEANING of π
    4. Circumference = ? (Animation)
    5. Circumference = ? (Animation II)
    6. 1 Radian: Clear Definition
    7. Radian Illustrator
    8. Quiz: Sketching Angles in Standard Position
    9. DEG to RAD and RAD to DEG Illustrator
    10. DEG to RAD and RAD to DEG: Question Generator
    11. Arc length: Quick Investigation
    12. Parallelogram: Area
    13. Triangle Area Action!!! (V2)
    14. Circle Area (By Peeling!)
    15. Arc Length and Area of a Sector (V1)
    16. Arc Length and Area of a Sector (V2)
    17. Area of a Sector
    18. Angular to Linear: Without Words
    19. YOUR Linear Speed?
26. Graphing and Writing Trigonometric Functions
    1. Unit Circle to Sine and Cosine Functions
    2. Tangent Function Exploration
    3. Cotangent Function Exploration
    4. Transforming Sine and Cosine Functions (1): Dynamic Illustrator
    5. Transforming Sine and Cosine Functions (2): Dynamic Illustrator
    6. Quiz: Graphing Sine & Cosine Functions (Amplitude & Vertical Shift Only)
    7. Writing Sine and Cosine Functions (with Amplitude & Vertical Shift Changes)
    8. Periodic Function Action!
    9. Transforming the Sine Function (All Transformations)
    10. Sine & Cosine Period Action (1)!
    11. Graphing Sine & Cosine Functions (I)
    12. Graphing Sine & Cosine Functions (II)
    13. Modeling with Trigonometric Functions
    14. Inverse Trig Functions: Intuitive Explorations
27. Proving Trig Identities
    1. Trig ID: Geometric Investigation
    2. New Trig IDs From Similar Right Triangles
    3. New Trig ID's from Similar Right Triangles (V2)
28. Advanced Topics
    1. Special Trigonometric Identities: Quick Exploration
    2. Law of Sines (& Area)
    3. SSA Theorem?
    4. Ambiguous Case (SSA) Illustrator: All Cases
    5. Law of Cosines: Discovery
29. Bearings (Applications)
    1. Bearing Illustrator (1)
    2. Bearing: Dynamic Illustration
    3. Bearing Illustrator (2)
    4. Bearings: Dynamic Illustrator
30. Vectors
    1. Vectors: Magnitude & Direction (I)
    2. Scaling Vectors
    3. Vector Addition
    4. Quiz: Adding Vectors Geometrically
    5. Vector Subtraction
31. 基本三角
    1. 銳角三角：sin, cos
    2. 銳角三角：tan
    3. 廣義角
    4. 廣義三角：sin, cos
    5. 廣義三角：tan
    6. COS 特別角
    7. 角度、弧度互換
    8. 三角函數圖解
    9. 0, 90, 180, 270 ± θ
    10. 弧度
    11. 弧度與角度
    12. 判斷三角形
    13. 時針與分針的夾角
    14. 三角函數值 (特別角)
32. 三角形公式
    1. 三角形面積公式 1/2 bc sinA
    2. 正弦定理
    3. 餘弦定理
33. 和角公式
    1. 向量的伸縮
    2. 向量合成
    3. 點座標旋轉公式
    4. 1+z² = (2cosθ) z
    5. 45 ° 的和角
    6. 旋轉的概念
34. 三角測量
    1. 立體測量：兩仰角
35. 函數圖形
    1. sin(x) 的函數圖形
    2. cos(x) 的圖形
    3. a sin(bx+c) + d 的圖形
    4. 三角函數圖形
    5. 三角函數圖形（全）
    6. Geometric Fourier Transform
    7. tan(x) = x
36. 參數式
    1. 橢圓參數式
    2. 兩圓動點的中點軌跡
    3. Cycloid
    4. Curtate Cycloid
    5. Epicycloid
    6. 極式：切線方向
    7. 直角座標轉為極座標
37. 三角恆等式
    1. cos(π/n)cos(2π/n)cos(3π/n) ... cos(nπ/n) = ?
    2. cos(α) + cos(β) + cos(γ) 的對稱性
38. 三角不等式
    1. -3/2 ≤ cosα + cosβ + cosγ ≤ 3
    2. -3/2 ≤ cosα + cosβ + cosγ ≤ 3
    3. -3 ≤ cosA+cosB+cosC ≤ 3/2
    4. 3/4 ≤ cos²A+cos²B+cos²C ≤ 3
    5. -1/8 ≤ cosα cosβ cosγ ≤ 1
    6. -1 ≤ cosA cosB cosC ≤ 1/8
    7. 0 ≤ sinA sinB sinC ≤(√3/2)³
    8. -(√3/2)³ ≤ sinα sinβ sinγ ≤ (√3/2)³
39. 相關問題
    1. 經過相同點的不同週期函數
    2. 交點的極限
    3. 等腰三角形內嵌矩形
    4. 三餘弦定理問題
    5. 17 邊形
    6. sinα + sinβ > 0 ?
    7. tan(α) tan(β) = ?
    8. 正三角形內一點到三頂點的距離
    9. 圓的外切圓
40. 歸檔
    1. 銳角三角函數
    2. 基本三角函數
    3. cos, sin 與單位圓