Trigonometry

Auston B Cron, Mar 5, 2014

Lessons to help understand trigonometric concepts...

Table of Contents

  1. 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
  2. Degrees-Radian Measures
    1. Degrees vs Radians
    2. Radian Units
    3. Basic Trig -360° x 360°
    4. Full Circle Protractors
  3. Unit Circle
    1. Creating a Unit Circle
    2. Unit Circle
    3. Unit CircleTriangles
    4. Unit Circle Triangles
    5. What class of Triangles use Pythagorean Theorem?
  4. 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
  5. 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
  6. 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
  7. 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

1.

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

1.1.

Basic Trig -360 x 360

This is a blank page set for students to graph trig functions easily by plotting the points by using the point tool. When finished plotting the student should try to write the function graphed.
The degree symbol is require for graphing: sin(x°), cos(x°), tan(x°) {PC can use <alt><o> or symbol menu α }[br][br]Available for all who desire to use...
– Auston B Cron

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2.

Degrees-Radian Measures

  • 1. Degrees vs Radians
  • 2. Radian Units
  • 3. Basic Trig -360° x 360°
  • 4. Full Circle Protractors

2.1.

Degrees vs Radians

Move the slider n to change the number of degrees or rays.[br][br]This comparison displays the difference of 30 degrees and 30 radians.[br][br]0 <= n <= 3600
Degrees vs Radians
– Auston B Cron

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3.

Unit Circle

  • 1. Creating a Unit Circle
  • 2. Unit Circle
  • 3. Unit CircleTriangles
  • 4. Unit Circle Triangles
  • 5. What class of Triangles use Pythagorean Theorem?

3.1.

Creating a Unit Circle

The instruction in Graphic2 are instructions to create this applet on you desktop. [br][br]Or you can erase and recreate in this window.
Have fun.
– Auston B Cron

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4.

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

4.1.

Find distance between Cities

Enter latitude of two cities on the same longitudinal line. The steps and work to find the distance will be shown and computed. This is designed to check homework problems.
– Auston B Cron

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5.

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

5.1.

Basic Terms in Geometry

This lessons reviews Basic Geometry Vocabulary with interactive displays of the vocabulary.[br][br]Point(s), Plane, Line, Segment, Ray, Angle, Side(s), Vertex, etc.
Additional resources to view:[br]Standard Position 01[br]Standard Position 01a[br]Coterminal Angles 01b
– Auston B Cron

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5.11.

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6.

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

6.1.

1st Definition of Trigonometry Functions

One way to define trigonometric function is by place a point in a coordinate plane allowing the distance to the origin to be a radius which determines the angle of the function.
1st Definition of Trigonometry Functions
– Auston B Cron

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6.11.

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6.14.

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6.18.

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6.19.

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6.20.

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6.21.

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6.22.

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7.

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

7.1.

Trigonometric Identity Explorer

Basic Trigonometry Functions[br]Reciprocal Identities[br]Quotient Identities[br]Pythagorean Identities[br]Negative Angle Identities[br]Sum and Difference Identities[br]Cofunction Identities[br]Double Angle Identities[br]Product-to-Sum Identities[br]Sum-to-Product Identities[br]Half Angle Identities
Review these Identities
– Auston B Cron

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