It is something of a mystery to me that we learn three Pythagorean Identities in Trigonometry but do not learn what triangles they relate to! Doesnt that strike you as odd, too? It seems that all memory of these triangles has disappeared from our text books and lessons. Early in our high school mathematics career, we learn Pythagoras Theorem and that it relates to right-angled triangles. Yet, here we have three fundamental and famous identities and most students (and likely most teachers) have no idea what triangles they describe. This video, and the one following it, contain my attempts to correct that omission. I believe that you will understand trigonometry much better if you learn this material. If you learn about each of the three triangles, you will understand all six trigonomeric ratios in a new way. As a bonus, you will remember the three identies MUCH more easily. In this video, I explain how to derive, understand and learn the identity tan²(θ) + 1 = sec²(θ). You will also learn an intuitive and graphical way of understanding and estimating the values of tan(θ) and sec(θ) given any angle θ. I hope you have quite an aha experience.
Posted on: Sat, 01 Nov 2014 15:35:21 +0000
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