4. Right Triangle Trigonometry (The Deep End)

Cofunction Identities! Shortcuts! Pythagorean Identities Gone Wild! Gratuitous insults from both SOH CAH TOA and a passing cabbie! Guest appearances from Pythagoras! Mumbling and grumbling about bad notation! Everybody happy on the inside! Come one, come all! This is the 4th of a sequence of supplementary videos for a trigonometry class taught from my book 𝑃𝑟𝑒𝑐𝑎𝑙𝑐𝑢𝑙𝑢𝑠 𝑀𝑎𝑑𝑒 𝐷𝑖𝑓𝑓𝑖𝑐𝑢𝑙𝑡. See my website https://bravernewmath.com for more information on my various books: 𝐹𝑢𝑙𝑙 𝐹𝑟𝑜𝑛𝑡𝑎𝑙 𝐶𝑎𝑙𝑐𝑢𝑙𝑢𝑠, 𝑇ℎ𝑒 𝐷𝑎𝑟𝑘 𝐴𝑟𝑡 𝑜𝑓 𝐿𝑖𝑛𝑒𝑎𝑟 𝐴𝑙𝑔𝑒𝑏𝑟𝑎, 𝑃𝑟𝑒𝑐𝑎𝑙𝑐𝑢𝑙𝑢𝑠 𝑀𝑎𝑑𝑒 𝐷𝑖𝑓𝑓𝑖𝑐𝑢𝑙𝑡, 𝐿𝑜𝑏𝑎𝑐ℎ𝑒𝑣𝑠𝑘𝑖 𝐼𝑙𝑙𝑢𝑚𝑖𝑛𝑎𝑡𝑒𝑑. The first three are available for sale as paperbacks at Amazon, and as pdfs at Lulu. (The Lobachevski book is available at Amazon and the American Mathematical Society) 0:00 Intro 0:28 Reciprocal Trig Functions (sec, csc, cot) 5:45 Cofunction Identities 13:22 a Right Triangle Shortcut 21:35 a Secondary Right Triangle Shortcut 24:32 Interlude with Spherical Coordinates 30:45 Tiptoeing Towards the Pythagorean Identities 31:10 Notation for Positive Powers of Trig Functions 34:08 the (Main) Pythagorean Identity 39:33 an Alternate Pythagorean Identity 43:21 the 3rd, and least loved, Pythagorean Identity 46:20 Can the 2 "Alternate" Pythag Ids be Understood Geometrically? 47:18 One Picture Revealing All 3 Pythagorean Identities