Trigonometric Functions + A Very Difficult Integral

If you're only here for the review of trigonometric functions but you're not ready for difficult integrals yet, you should only watch the first 20 minutes or so of this video! In them, I'm going to summarize all the relevant features of the trigonometric functions, like the amplitude, principal axis, and period, describing them in terms of graphic transformations (vertical translation, vertical stretch, vertical reflection, horizontal translation and stretch).

If, on the other hand, you're into difficult integrals, please stay until the end, because this one was a particularly pretty one and I really like the techniques that I had to use in order to find an answer :-)

But WHY is the horizontal axis doing everything backwards??    • Graphic Transformations - But WHY is the h...  

00:00 - Intro
01:28 - Trigonometric Functions
17:27 - Exercises
22:26 - Graphic Adding
25:52 - Exercises
39:41 - Graphic Multiplying
43:32 - The Integral of Cosine Squared
46:24 - Starting the Difficult Integral
52:30 - Complex Numbers
56:30 - Finishing the Difficult Integral