Pre-calculus

Jila, Feb 8, 2018

Table of Contents

  1. Chapter One, Functions
    1. 1.2- Domain and Range - Piecewise Defined Graphing
    2. 1.2: An open box with constant volume
    3. 1.3-Rate of Change and Behavior of Graph
    4. 1.3: Slope of Secant Line.
    5. 1.5- Function Transformations- Order of Transformations
    6. 1.6-Absolute Value Functions
  2. Chapter Two, Linear Functions
    1. 2.1-Right triangle paradox, Created by Sonom
    2. 2.3-Modeling with Linear Functions
  3. Chapter Three, Rational and Polynomial Functions
    1. 3.2 Optimization
    2. 3.2: Optimization: Inscribe a rectangle in a triangle
    3. 3.3-Polynomial Functions
    4. 3.4- Graph of a polynomial
    5. 3.6-Zeros of Polynomial Functions-Roots of a polynomial of degree 4
  4. Chapter Four, Exponential Functions
    1. 4.1: Exponential Functions
    2. 4.2: Graphing Exponential Functions
    3. 4.2: Graphing Exponential Functions
  5. Chapter Five: Trigonometric Functions
    1. 5.1: Angles in Unit Circle
    2. 5.1: Angular Velocity
    3. 5.2: The unit Circle- Reference Angles
    4. 2.6: Calculus 5.4: Precalculus How an angle and its sine are related (angles in first quadrant)
  6. Chapter Six: Periodic Functions
    1. 6.1: Ferris wheel
    2. 6.1: Graphing a Free Harmonic Motion(Spring)
  7. Chapter Seven, Trigonometric Identities and Equations
    1. 7.2: Proof of Sine and Cosine of a Sum
    2. 7.6: Police Chase
    3. 7.6: Police Chase
    4. 7.5: Graphing Damped Harmonic Motion (Spring)
  8. Chapter Eight, Further Applications of Trigonometry
    1. 8.1: SSA Sides a and b are given. Angle A is given.
    2. 8.3: Polar Coordinates
    3. 8.4: Polar Coordinates: Graphing r=a+/- bcos(theta)
    4. 8.4: Rose Curve
    5. 8.4: Drawing Limacons using Other Tools
    6. 8.7: Parametric Heart, Click Play and watch.
    7. 8.7: Trace of a point on a wheel. Click play on the slider.
    8. 8.7: Throwing a baseball
    9. 8.7: Parametric Curves
    10. 8.7: Parametriziation of Cardioid
    11. 8.7: Oval
    12. 8.7: What is theta in Ellipse parametrization?
    13. 8.4: Graphing a+ b cos (kt)
    14. Rose Pedals
  9. Chapter Ten, Analytic Geometry
    1. 10.1: Ellipse
    2. 10.1: The area of a rectangle inscribed in an ellipse
    3. 10.2 Hyperbola
    4. 10.3: Parabolas
    5. 10.3: Concave Mirrors

1.

Chapter One, Functions

  • 1. 1.2- Domain and Range - Piecewise Defined Graphing
  • 2. 1.2: An open box with constant volume
  • 3. 1.3-Rate of Change and Behavior of Graph
  • 4. 1.3: Slope of Secant Line.
  • 5. 1.5- Function Transformations- Order of Transformations
  • 6. 1.6-Absolute Value Functions

1.1.

1.2- Domain and Range - Piecewise Defined Graphing

Piecewise Defined
– Jila

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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2.

Chapter Two, Linear Functions

  • 1. 2.1-Right triangle paradox, Created by Sonom
  • 2. 2.3-Modeling with Linear Functions

2.1.

2.1-Right triangle paradox, Created by Sonom

Rearrange the first shape into the second one. Are the two shapes congruent? Explain why? This is a copy of work created by https://www.geogebra.org/u/sonom by Sonom.
– Jila, sonom

2.2.

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3.

Chapter Three, Rational and Polynomial Functions

  • 1. 3.2 Optimization
  • 2. 3.2: Optimization: Inscribe a rectangle in a triangle
  • 3. 3.3-Polynomial Functions
  • 4. 3.4- Graph of a polynomial
  • 5. 3.6-Zeros of Polynomial Functions-Roots of a polynomial of degree 4

3.1.

3.2 Optimization

– Jila

3.2.

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3.3.

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3.4.

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3.5.

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4.

Chapter Four, Exponential Functions

  • 1. 4.1: Exponential Functions
  • 2. 4.2: Graphing Exponential Functions
  • 3. 4.2: Graphing Exponential Functions

4.1.

4.1: Exponential Functions

The Instantaneous rate of change is the proportional to the value of the function at any point.
– Jila

4.2.

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4.3.

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5.

Chapter Five: Trigonometric Functions

  • 1. 5.1: Angles in Unit Circle
  • 2. 5.1: Angular Velocity
  • 3. 5.2: The unit Circle- Reference Angles
  • 4. 2.6: Calculus 5.4: Precalculus How an angle and its sine are related (angles in first quadrant)

5.1.

5.1: Angles in Unit Circle

– Jila

5.2.

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5.3.

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5.4.

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6.

Chapter Six: Periodic Functions

  • 1. 6.1: Ferris wheel
  • 2. 6.1: Graphing a Free Harmonic Motion(Spring)

6.1.

6.1: Ferris wheel

– Jila

6.2.

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7.

Chapter Seven, Trigonometric Identities and Equations

  • 1. 7.2: Proof of Sine and Cosine of a Sum
  • 2. 7.6: Police Chase
  • 3. 7.6: Police Chase
  • 4. 7.5: Graphing Damped Harmonic Motion (Spring)

7.1.

7.2: Proof of Sine and Cosine of a Sum

Slide the slider to see the steps of the proof.
Instructions
– Jila

7.2.

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7.3.

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7.4.

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8.

Chapter Eight, Further Applications of Trigonometry

  • 1. 8.1: SSA Sides a and b are given. Angle A is given.
  • 2. 8.3: Polar Coordinates
  • 3. 8.4: Polar Coordinates: Graphing r=a+/- bcos(theta)
  • 4. 8.4: Rose Curve
  • 5. 8.4: Drawing Limacons using Other Tools
  • 6. 8.7: Parametric Heart, Click Play and watch.
  • 7. 8.7: Trace of a point on a wheel. Click play on the slider.
  • 8. 8.7: Throwing a baseball
  • 9. 8.7: Parametric Curves
  • 10. 8.7: Parametriziation of Cardioid
  • 11. 8.7: Oval
  • 12. 8.7: What is theta in Ellipse parametrization?
  • 13. 8.4: Graphing a+ b cos (kt)
  • 14. Rose Pedals

8.1.

8.1: SSA Sides a and b are given. Angle A is given.

Move A in and out of the circle to get different choices for SSA.
What does this mean?
[list][*]When the side adjacent to the angle [b]is smaller that the other given side[/b] (inside the circle), you will get at most one triangle.[/*][*]When the side adjacent to the angle [b]is bigger than the other given side[/b] (outside the circle), you can get up to 2 triangles. [/*][/list]
– Jila

8.2.

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8.3.

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8.4.

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8.5.

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8.6.

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8.7.

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8.8.

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8.9.

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8.10.

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8.11.

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8.12.

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8.13.

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8.14.

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9.

Chapter Ten, Analytic Geometry

  • 1. 10.1: Ellipse
  • 2. 10.1: The area of a rectangle inscribed in an ellipse
  • 3. 10.2 Hyperbola
  • 4. 10.3: Parabolas
  • 5. 10.3: Concave Mirrors

9.1.

10.1: Ellipse

Description:
The total distance between a point on an ellipse to the two foci stays the same. (Move point X to see that.)
– Jila

9.2.

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9.3.

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9.4.

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9.5.

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