====== Trigonometric Functions ====== * [[https://betterexplained.com/articles/intuitive-trigonometry/|How To Learn Trigonometry Intuitively]] by Kalid Azad * [[https://betterexplained.com/articles/intuitive-understanding-of-sine-waves/|Intuitive Understanding of Sine Waves]] by Kalid Azad * [[https://betterexplained.com/articles/law-of-cosines/|Intuition For The Law Of Cosines]],[[https://betterexplained.com/articles/law-of-sines/|Intuition For The Law Of Sines]] * [[http://www.businessinsider.com/7-gifs-trigonometry-sine-cosine-2013-5?IR=T|7 Animated GIFs That Will Make You Instantly Understand Trigonometry]] [{{ :basic_notions:trigonometricfunctions.png?nolink |Source: http://advancedmathyoungstudents.com/blog/2017/10/06/that-trigonometry-diagram-again/}}] ---- * https://problemproblems.wordpress.com/2018/04/23/teaching-right-triangle-trigonometry-as-a-series-of-problems/ The motto in this section is: //the higher the level of abstraction, the better//.
Imagine Bob The Alien visits Earth to study our species. Without new words, humans are hard to describe: “There’s a sphere at the top, which gets scratched occasionally” or “Two elongated cylinders appear to provide locomotion”. After creating specific terms for anatomy, Bob might jot down typical body proportions: * The armspan (fingertip to fingertip) is approximately the height * A head is 5 eye-widths wide * Adults are 8 head-heights tall How is this helpful? Well, when Bob finds a jacket, he can pick it up, stretch out the arms, and estimate the owner’s height. And head size. And eye width. One fact is linked to a variety of conclusions. Even better, human biology explains human thinking. Tables have legs, organizations have heads, crime bosses have muscle. Our biology offers ready-made analogies that appear in man-made creations. Now the plot twist: you are Bob the alien, studying creatures in math-land! Generic words like “triangle” aren’t overly useful. But labeling sine, cosine, and hypotenuse helps us notice deeper connections. And scholars might study haversine, exsecant and gamsin, like biologists who find a link between your tibia and clavicle. And because triangles show up in circles… {{ :basic_tools:vitruvian-triangle.png?nolink |}} …and circles appear in cycles, our triangle terminology helps describe repeating patterns! Trig is the anatomy book for “math-made” objects. If we can find a metaphorical triangle, we’ll get an armada of conclusions for free. [[https://betterexplained.com/articles/intuitive-trigonometry/|How To Learn Trigonometry Intuitively]] by Kalid Azad