Trigonometry/Teachers Notes/Khan Academy Videos
The Khan Academy Videos
editThe Khan Academy is a not-for-profit educational organization providing a free on-line collection of more than 2,000 short videos on mathematics, science, history, and economics.
- Book 1 of Trigonometry is designed to complement the Khan Academy Trigonometry videos in a number of ways:
- Both are pre-calculus. They match in level of prior mathematical knowledge required.
- In both algebra is done step by step. The assumption is that the student is still relatively new to algebra.
- Free to use exercises on the Khan Academy website provide practice in the core skills and tracking of progress.
Whilst both book and the videos can be used stand-alone, the Khan Academy videos can help with absorbing the material. Equally the book can be a help to students following the video course adding extra problems, examples, applications and alternative proofs.
The Trigonometry Book 1 may not be an ideal complement to the Khan Academy Videos. The 'for Enthusiasts' section, whilst still pre-calculus, takes trigonometry beyond where most conventional trigonometry textbooks would go. The for-enthusiasts material on the CORDIC algorithm and on Delaunay triangulations, for example, is motivated by computer applications, whilst the exercise on the distance between Tokyo and New York relates latitude and longitude to trigonometry. The main part of book 1 takes an in some way more sophisticated approach to proof than is normal at this level. It touches on the possibility of different proofs of the same theorem, on how a proof might have been discovered and on what assumptions are needed for a proof to work.
Trigonometry Book 2 requires some knowledge of calculus. It is suggested to do the Calculus wikibook before starting on it. Book 2 covers more advanced topics like relation of complex numbers to trigonometric functions, Fourier series, hyperbolic functions.
This is the complete list of Khan Academy Trigonometry videos.
These tables are a work in progress. Until they are more complete they should be taken with a grain of salt. |
Geometry Series Videos:
The geometry videos are 90% about trigonometry (but without sin cos and tan)
| Khan Academy Video | What's in the Khan Video and what's in the book? | Page in this book |
|---|---|---|
|
Angles of a triangle sum to 180 Degrees | |
|
Angles of a triangle sum to 180 Degrees | |
|
Angles of a triangle sum to 180 Degrees | |
|
||
|
||
| Uses angles of a triangle sum to 180 degrees, exterior angle of a triangle, and similar triangles. | Angles of a triangle sum to 180 Degrees | |
|
See also Exercise: Congruent Triangles | Angles of a triangle sum to 180 Degrees |
|
Angles of a triangle sum to 180 Degrees | |
|
Angles of a triangle sum to 180 Degrees | |
|
||
|
Geometry; not part of Trigonometry book. | |
|
Geometry; not part of Trigonometry book. | |
|
The Pythagorean Theorem | |
|
Proof: Pythagorean Theorem | |
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
Trigonometry Series Videos:
These are the videos that most closely correspond to the book. These are where sin cos and tan are first used.
| Khan Academy Video | What's in the Khan Video and what's in the book? | Page in this book |
|---|---|---|
| Soh-Cah-Toa (Sine and Cosine) | Soh-Cah-Toa | |
| Soh-Cah-Toa (starting with Tan). | Soh-Cah-Toa | |
| Explanation of radians and how to convert to and from degrees. | Radians | |
|
||
|
||
| In the book there is an exercise to plot sine and cosine, then later sine and cosine are defined in terms of the unit circle. | Plotting (Cos t, Sin t) and | |
| Plotting (Cos t, Sin t) and | ||
| Graphs of Sine and Cosine Functions | ||
| Graphs of Sine and Cosine Functions | ||
|
Graphs of Sine and Cosine Functions | |
| Graphs of Sine and Cosine Functions | ||
|
||
|
||
| The book uses the same proof as Khan Academy video. Book has exercises to practice using the formula and an exercise for checking understanding of the proof. Also gives an explanation of how you would come up with the diagram. | Addition Formula for Sines | |
| The book uses the same diagram and a very similar proof to the Khan Academy video. Also has a worked example showing that we can derive one from the other and an exercise (going the other way). | Addition Formula for Cosines | |
|
||
|
||
| Solve SAS. | Solving Triangles Given SAS | |
| Solve SAS (part 2). | Solving Triangles Given SAS | |
| Law of Cosines | ||
|
In this Khan video a solve SAS problem is presented as a navigation problem, similar in some ways to what is intended for Worked Example: Oil Tanker Arriving in Port. | Solving Triangles Given SAS |
| Law of Sines | ||
| Book has same problem as in video. | Worked Example: Ferris Wheel Problem | |
|
||
|
Solve | |
|
Nothing on Polar coordinates in the book yet. | |
|
||
|
||
|
The book is very incomplete on inverse trig functions at the moment. | Inverse Trigonometric Functions |
|
Inverse Trigonometric Functions | |
|
Inverse Trigonometric Functions | |
|
Remembering Trig Formulas |
California Standards Test: Geometry:
Worked examples. Salman Khan does the 80 problems from the released questions from the California Standards Test for Geometry. Test at http://www.cde.ca.gov/ta/tg/sr/documents/rtqgeom.pdf.
| Khan Academy Video | What's in the Khan Video and what's in the book? | Page in this book |
|---|---|---|
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|