③ today i bring you: an interactive visualization of the six trig functions, which imo makes them make way more sense than basically anything i've seen https://c.eev.ee/viz/trig-functions.html
@eevee oh gods thank fuck I always feel like I'm wasting everyone's time when I draw this up
Fun part: this also immediately proves all the pythagorean identities!
@eevee Yup! Drop cos to the x-axis where it belongs. Then look at ANY right triangle with the unit radius as one of its sides and tell me what you now know.
@eevee side note: GODS do I ever fucking wish my actual students were this interested but the joy and curiosity and aesthetic appreciation of math have long since been beaten out of them :S
@CoronaCoreanici yes i know i just made a thing that had to make use of this property 8)
i mean there are similar triangles everywhere and that would be enough to prove it, except i don't see a similar one for the x side?
@eevee (it's actually very unimportant though it is actually a thing that was once important enough to be included in tables of trig functions)
@Felthry yeah i remember reading about these, the wikipedia article is actually the one place that has a diagram showing them all semi-clearly
This whole list is a trip. https://en.wikipedia.org/wiki/List_of_trigonometric_identities#Historical_shorthands
@eevee so these functions are all like...lengths of chords or whatever. Interesting. My high school geometry teacher kinda sucked, on top of math education in the us being wack anyway. Super interesting graphic, thanks for sharing.
Maybe now I can remember which is which. That makes more sense than any representation I have ever seen.
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