Trigonometry/Teachers Notes/Khan Academy Videos

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The Khan Academy Videos[edit]

The 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.



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
  • Introduction to angles
Angles of a triangle sum to 180 Degrees
  • Angles (part 2)
Angles of a triangle sum to 180 Degrees
  • Angles (part 3)
Angles of a triangle sum to 180 Degrees
  • Angles formed between transversals and parallel lines
  • Angles of parallel lines 2
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

Exercise: Chasing Angles

  • Similar triangles
See also Exercise: Congruent Triangles Angles of a triangle sum to 180 Degrees
  • Similar triangles (part 2)
Angles of a triangle sum to 180 Degrees
  • Angle Game (part 2)
Angles of a triangle sum to 180 Degrees
  • Area and Perimeter
  • Circles: Radius, Diameter and Circumference
Geometry; not part of Trigonometry book.
  • Area of a circle
Geometry; not part of Trigonometry book.
  • The Pythagorean Theorem
The Pythagorean Theorem
  • Pythagorean Theorem II
Proof: Pythagorean Theorem
  • 45-45-90 Triangles
  • Intro to 30-60-90 Triangles
  • 30-60-90 Triangles II
  • Heron's Formula
  • Part 1 of Proof of Heron's Formula
  • Part 2 of the Proof of Heron's Formula
  • An inscribed angle is half of a central angle that subtends the same arc
  • Area of Inscribed Equilateral Triangle (some basic trig used)
  • Right Triangles Inscribed in Circles (Proof)
  • Area of Diagonal Generated Triangles of Rectangle are Equal


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
  • Using Trig Functions
  • Using Trig Functions Part II
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

The Unit Circle

Plotting (Cos t, Sin t) and

The Unit Circle

Graphs of Sine and Cosine Functions
Graphs of Sine and Cosine Functions
  • Graphing trig functions
Graphs of Sine and Cosine Functions
Graphs of Sine and Cosine Functions
  • Determining the equation of a trigonometric function
  • Trigonometric Identities
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
  • Trig identities part 2 (part 4 if you watch the proofs)
  • Trig identities part 3 (part 5 if you watch the proofs)
Solve SAS. Solving Triangles Given SAS
Solve SAS (part 2). Solving Triangles Given SAS
Law of Cosines
  • Navigation Word Problem
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
  • Ferris Wheel Trig Problem (part 2)
  • Fun Trig Problem
Solve \displaystyle 3\sin^2x=1+\cos x
  • Polar Coordinates 1
Nothing on Polar coordinates in the book yet.
  • Polar Coordinates 2
  • Polar Coordinates 3
  • Inverse Trig Functions: Arcsin
The book is very incomplete on inverse trig functions at the moment. Inverse Trigonometric Functions
  • Inverse Trig Functions: Arctan
Inverse Trigonometric Functions
  • Inverse Trig Functions: Arccos
Inverse Trigonometric Functions
  • Trigonometry Identity Review/Fun
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
  • CA Geometry: deductive reasoning
  • CA Geometry: Proof by Contradiction
  • CA Geometry: More Proofs
  • CA Geometry: Similar Triangles
  • CA Geometry: Similar Triangles
  • CA Geometry: More on cogruent and similar triangles
  • CA Geometry: Triangles and Parallelograms
  • CA Geometry: Area, Pythagorean Theorem
  • CA Geometry: Area, Circumference, Volume
  • CA Geometry: Pythagorean Theorem, Area
  • CA Geometry: Exterior Angles
  • CA Geometry: Deducing Angle Measures
  • CA Geometry: Pythagorean Theorem, Compass Constructions
  • CA Geometry: Compass Construction
  • CA Geometry: Basic Trigonometry
  • CA Geometry: More Trig
  • CA Geometry: Circle Area Chords Tangent
  • CA Geometry: Secants and Translations