i am doing an ADVENT CALENDAR
πŸŽ„ c.eev.ee/advent-2019/ πŸŽ„

i intend to make and release one thing every single day until christmas!
no idea what they'll be, i'm making this up as i go. wish me luck!

(also stopping dev log for a bit! more explanation: patreon.com/posts/32045494)

β‘’ 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 c.eev.ee/viz/trig-functions.ht

@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 (hint: tangent lines to circles are perpendicular to the radii they intersect.)

@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?

@efi @eevee don't worry, three are just 1/ the other three XD

sec(x) = 1/cos(x)
csc(x) = 1/sin(x)
cot(x) = 1/tan(x)

and ofc
tan(x) = sin(x) / cos(x)
sin(x) = cos(x - Ο€/2) ie just shifted sideways a bit on the wavey graph :3

so really there's always only been one trig function this whooole time :^3

@efi @eevee *throws hyperbolic blanket over them* nuuuuuu don't go to the darkbolic side!


That would be a good other visual aid though...


(no don't feel pressured Eevee XD )

@efi @eevee but in seriousness I think if you add them, there are three core functions

1 (circular) trig
2 hyperbolic trigs

(which ones are "core" up to you ofc :3 )

@eevee But what about the most important trig function of them all, the haversine?

@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

@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.

@eevee this is exactly what I was looking for! thanks! I love you so much right now hahah

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