Trigonometría e Introducción a la Estadística

Geogebra Cumbres, Jan 27, 2016

Math 4th Semester Prepa Tec Campus Cumbres

Table of Contents

  1. Basic Concepts on Trigonometry
    1. Angles Created by Two Parallel Lines Cut by a Transversal
    2. Radian conversion
    3. Basic Angle Definitions .
    4. Coterminal and Reference Angles
    5. Arc Length and Sector Area
  2. Trigonometric Ratios
    1. Trigonometric Ratios
    2. Trig Functions of special angles on the unit circle
  3. Solving Triangles
    1. Classifying triangles - segments
    2. Right Angled Triangles
    3. Review and Practice Solving Oblique Triangles
    4. Law of Sine Proof
    5. Law of Cosine - Proof
    6. SAS Sliders
    7. SSS Sliders
    8. SSA Law of Sines Ambiguous Case
  4. Trigonometric Functions and Trigonometric Inverse Functions
    1. Sine and Cosine Components
    2. Sine and Cosine Transformations
    3. Transformation of Sine and Cosine Graphs
    4. Inverse trigonometric functions
  5. Trigonometric Identities
    1. Understand Trigonometric Identities
    2. trig expressions by Tom Owsiak
    3. Proving Trigonometric identity: sin(2x) = 2sin(x)cos(x)
    4. Sum and difference formulas
    5. Proving sum and difference Identities
    6. The double angle formulae
  6. Trigonometric Equations
    1. Graphing Trigonometric Functions: Sin
    2. GeoGebra Like a Graphing Calculator Equations, Inequalities.
  7. Modeling Using Sinusoidial Graphs
    1. Sinusoidal Motion
    2. Graphs of Composite Trigonometric Functions
    3. Phasor Diagram and Sinusoid
  8. Introduction to Statistics
    1. Central Tendencies
    2. Example 3

1.

Basic Concepts on Trigonometry

[list] 1.- Parallel lines crossed by a diagonal 2.- Angles: Radians and Degrees 3.- Angles: Basic Concepts 4.- Complementary, Supplementary and Conjugate Angles 5.- Coterminal and Reference Angles 6.- Arc Length and Sector of a Circle [/list]

  • 1. Angles Created by Two Parallel Lines Cut by a Transversal
  • 2. Radian conversion
  • 3. Basic Angle Definitions .
  • 4. Coterminal and Reference Angles
  • 5. Arc Length and Sector Area

1.1.

Angles Created by Two Parallel Lines Cut by a Transversal

Types of Angles Created by Two Parallel Lines Cut by a Transversal
Check the boxes to see different types of angles created by two parallel lines cut by a transversal.
– Breck Jacobs

1.2.

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1.3.

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1.4.

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1.5.

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2.

Trigonometric Ratios

[list] [*]Trigonometric Ratio 1 [*]Special Angles [*]Trigonometric Ratios 2 Any Angle [/list]

  • 1. Trigonometric Ratios
  • 2. Trig Functions of special angles on the unit circle

2.1.

Trigonometric Ratios

– Toh Wee Teck

2.2.

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3.

Solving Triangles

[list] [*]Classifying Triangles [*]Solving Right Triangles [*]Applications: Right Triangles [*]Solving Oblique Triangles [*]Laws of Sines [*]Law of Cosines [*]Application: Solving Triangles [/list]

  • 1. Classifying triangles - segments
  • 2. Right Angled Triangles
  • 3. Review and Practice Solving Oblique Triangles
  • 4. Law of Sine Proof
  • 5. Law of Cosine - Proof
  • 6. SAS Sliders
  • 7. SSS Sliders
  • 8. SSA Law of Sines Ambiguous Case

3.1.

Classifying triangles - segments
– khurley1

3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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3.7.

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3.8.

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4.

Trigonometric Functions and Trigonometric Inverse Functions

[list] [*]Sines and Cosines [*]Inverse Functions [/list]

  • 1. Sine and Cosine Components
  • 2. Sine and Cosine Transformations
  • 3. Transformation of Sine and Cosine Graphs
  • 4. Inverse trigonometric functions

4.1.

Sine and Cosine Components

Sine and Cosine Components
– GeoGebra Materials Team

4.2.

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4.3.

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4.4.

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5.

Trigonometric Identities

[list] [*]Identities [*]Simplifying Trigonometic Expressions [*]Verifying Trigonometric Identities [*]Sum and Difference Formulas [*]Double Angles [/list]

  • 1. Understand Trigonometric Identities
  • 2. trig expressions by Tom Owsiak
  • 3. Proving Trigonometric identity: sin(2x) = 2sin(x)cos(x)
  • 4. Sum and difference formulas
  • 5. Proving sum and difference Identities
  • 6. The double angle formulae

5.1.

Understand Trigonometric Identities

[color=#1551b5]Submitted by Mr. Donald C. Albin Jr.[/color] Professional Educator [url]www.donaldalbin.99k.org[/url] How to make physical sense of the trigonometric identities. [b]Directions[/b] [list] [*]Click a check-box next to a trigonometric identity in order to show curves that will help with visualization. [/list]

[b]Questions to promote inquiry[/b] [list] [*]Explain why each trigonomic identity makes sense, graphically. [*]How can you relate each of these identities to the unit circle? [/list]
– Donald C. Albin Jr.

5.2.

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5.3.

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5.4.

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5.5.

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5.6.

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6.

Trigonometric Equations

[list] [*]Solving Trigonometric Equations Algebraically [*]Solving Trigonometric Equations by Graphing [*]Reasoned Problems [/list]

  • 1. Graphing Trigonometric Functions: Sin
  • 2. GeoGebra Like a Graphing Calculator Equations, Inequalities.

6.1.

Graphing Trigonometric Functions: Sin

Open a new widow, show the Algebra View and the Graphics View. 1. Begin by creating three sliders: a_1, ω_1, and φ_1 2. Enter the sine function: g(x)= a_1 sin(ω_1 x + φ_1) 3. Create three more sliders: a_1, ω_1, and φ_1 4. Enter another sine function: h(x)= a_2 sin(ω_2 x + φ_2) 5. Create the sum of both functions: sum(x) = g(x) + h(x)
– Jose Arturo Gomez Velasquez

6.2.

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7.

Modeling Using Sinusoidial Graphs

[list] [*]Applications of sinusoidial graphs [*]Modeling without using technology [*]Modeling using technology [*]Research and modeling using sinusoidal graphs [/list]

  • 1. Sinusoidal Motion
  • 2. Graphs of Composite Trigonometric Functions
  • 3. Phasor Diagram and Sinusoid

7.1.

Sinusoidal Motion

– Lenore Horner

7.2.

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7.3.

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8.

Introduction to Statistics

[list] [*]Introduction to Statistic [*]Frequency Tables [*]Graphic Representation [*]Measures of Central Tendency [*]Measures of Dispersion [/list]

  • 1. Central Tendencies
  • 2. Example 3

8.1.

Central Tendencies
– John Golden, cwinske

8.2.

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