Trigonometry Applets

Chip Rollinson, Oct 21, 2019

Table of Contents

  1. Triangle Trig
    1. Right Triangle Trigonometry Ratios
    2. Law of Sines - Ambiguous Case
    3. Law of Cosines - Geometric Interpretation
    4. Proof without words: Law of cosinus
    5. Applied trigonometry: the larger of the river
  2. Circular Trig & Waves
    1. What is a radian?
    2. Circular Trigonometry Definitions
    3. Trigonometry Ratio Graph from Unit Circle
    4. Sine Wave Sounds
    5. Trig Circle: Coordinates of Special Angle Values
    6. Trigonometry - Geometric Definitions in a Unit Circle
    7. Trigonometry - Pythagorean Identities Geometrically
  3. Sum/Difference Formulas
    1. Sine & Cosine of a Sum: Discovery
    2. Sine and Cosine Sum and Difference Proofs
  4. Misc. Other Trig Stuff
    1. Polar vs Cartesian Functions
    2. Interactive Polygonal Sinusoids
    3. Spline Trigonometry
    4. Zeros of sin(lnx)
    5. Trig Identities from Euler's Formula

1.

Triangle Trig

  • 1. Right Triangle Trigonometry Ratios
  • 2. Law of Sines - Ambiguous Case
  • 3. Law of Cosines - Geometric Interpretation
  • 4. Proof without words: Law of cosinus
  • 5. Applied trigonometry: the larger of the river

1.1.

Right Triangle Trigonometry Ratios

– Chip Rollinson

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.

Circular Trig & Waves

  • 1. What is a radian?
  • 2. Circular Trigonometry Definitions
  • 3. Trigonometry Ratio Graph from Unit Circle
  • 4. Sine Wave Sounds
  • 5. Trig Circle: Coordinates of Special Angle Values
  • 6. Trigonometry - Geometric Definitions in a Unit Circle
  • 7. Trigonometry - Pythagorean Identities Geometrically

2.1.

What is a radian?

Based on a gif from a "How Things Work" Twitter post[br]https://twitter.com/ThingsWork/status/822177097837907969
– Chip Rollinson

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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3.

Sum/Difference Formulas

  • 1. Sine & Cosine of a Sum: Discovery
  • 2. Sine and Cosine Sum and Difference Proofs

3.1.

Sine & Cosine of a Sum: Discovery

[color=#000000]There are 8 expressions shown off to the right.  [/color]Your job is to carefully drag each expression (label) next to the segment (in the figure) whose length is given by this expression.  [br][br]After doing so, please answer the 2 questions that follow.
Given what you see in your diagram, write an equivalent expression for [math]\sin\left(\alpha+\beta\right)[/math].
Given what you see in your diagram, write an equivalent expression for [math]\cos\left(\alpha+\beta\right)[/math].
– Tim Brzezinski

3.2.

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4.

Misc. Other Trig Stuff

  • 1. Polar vs Cartesian Functions
  • 2. Interactive Polygonal Sinusoids
  • 3. Spline Trigonometry
  • 4. Zeros of sin(lnx)
  • 5. Trig Identities from Euler's Formula

4.1.

Polar vs Cartesian Functions

Be sure to click on the square button in the lower right corner to expand this applet to full screen...
Cartesian to Polar demonstration via wrapping by [url=https://www.geogebra.org/u/jeromeawhite]jeromeawhite[/url]...
– talljerome, Chip Rollinson

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4.3.

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4.4.

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4.5.

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