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basic_tools:trigonometric_functions [2017/12/16 12:55] jakobadmin ↷ Page moved from basic_notions:trigonometric_functions to basic_tools:trigonometric_functions |
basic_tools:trigonometric_functions [2018/04/25 17:26] (current) jakobadmin [Trigonometric Functions] |
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====== Trigonometric Functions ====== | ====== Trigonometric Functions ====== | ||
- | <tabbox Why is it interesting?> | ||
- | <tabbox Layman> | + | <tabbox Intuitive> |
+ | |||
+ | |||
+ | * [[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]] | ||
- | <note tip> | ||
- | Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party. | ||
- | </note> | ||
| | ||
- | <tabbox Student> | + | <tabbox Concrete> |
[{{ :basic_notions:trigonometricfunctions.png?nolink |Source: http://advancedmathyoungstudents.com/blog/2017/10/06/that-trigonometry-diagram-again/}}] | [{{ :basic_notions:trigonometricfunctions.png?nolink |Source: http://advancedmathyoungstudents.com/blog/2017/10/06/that-trigonometry-diagram-again/}}] | ||
- | + | ||
- | <tabbox Researcher> | + | ---- |
+ | |||
+ | * https://problemproblems.wordpress.com/2018/04/23/teaching-right-triangle-trigonometry-as-a-series-of-problems/ | ||
+ | |||
+ | |||
+ | <tabbox Abstract> | ||
<note tip> | <note tip> | ||
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- | <tabbox Examples> | + | <tabbox Why is it interesting?> |
- | --> Example1# | + | <blockquote>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”. | |
- | <-- | + | |
- | --> Example2:# | + | 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 | ||
- | <tabbox FAQ> | + | |
- | + | How is this helpful? | |
- | <tabbox History> | + | |
+ | 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. | ||
+ | <cite>[[https://betterexplained.com/articles/intuitive-trigonometry/|How To Learn Trigonometry Intuitively]] by Kalid Azad</cite></blockquote> | ||
</tabbox> | </tabbox> | ||