Trigonometry-MrDownes

Author:: Ronan Downes

Topic:: Trigonometry

Trigonometry-MrDownes

Table of Contents

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

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