Question

I'm wondering why ratios have the relation with angles with sine and cosine. How did mathematicians thought about it when they defined sine and cosine?

Answer 1

@ganeshie8

Answer 2

why sine is the ratio of the opposite to hypo
why it has to be that way lol

Answer 3

@satellite73
what do you think! lol

Answer 4

You may wish to have a chat with ancient Egyptians and others of the era. The had to build things. They got tired of calculating new things, since it was amazingly tedious. Thye began to build tables of values and made their lives better. Really, until the advent of the computer or hand-held calculator (I first touched one in 1974), it may have been someone's life's work to produce a good table.

Answer 5

well if i could, I would definitely ask the ones that came up with it hehe

Answer 6

I wonder if trig ratios were first discovered or the pythegorean thm

Answer 7

hehe Don't ask me!? no idea!
but pyth thm has been found in many ancient tablets than trig ratios

Answer 8

You can always go ask Rutgers University.

http://www.math.rutgers.edu/~cherlin/History/Papers2000/hunt.html

Answer 9

eh rutgers! good suggestion, the university is near where i live lol

Answer 10

thanks @tkhunny

Answer 11

concepts of triangles/polygons/polyhedra must precede trig ratios i guess.. trig ratios is a pretty natural idea, we would have discovered trig ratios or something similar on our own if we got cast away'ed to some island and had all the leisure time to look at surroundings and use our math reasoning to solve problems. math history is really an interesting subject... you might like to google other related stuff like greek architecture, parthenon construction, golden ratio and other stuff...

Answer 12

yeah! I'm kinda interested thanks i will check out those titles
so if we make some calculation and use the facts we know we would end up with trig ratio
verified

Answer 13

this video doesn't talk about ratios, but talks more about ancient greek architecture :
https://www.youtube.com/watch?v=ICmlfXZnkns

Answer 14

Oh nice! I enjoy those documentaries
I appreciate it
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when can a student here in us take a math history course? do you have any idea

Answer 15

not so sure, if you have extra time, below course is really good. it touches many general topics and talks about how they are developed over centuries :

https://www.youtube.com/watch?v=dW8Cy6WrO94

focus is mainly on number theory and geometry

Answer 16

oh Wildberger! I'm following some of his lectures

Answer 17

by the way that professor doesn't believe in the idea of infinity
and real numbers lol. He has really good videos

Answer 18

Oh nice I like his way to teaching too, yeah I remember watching a video where he confesses that he doesnt believe in infinite sets...

Answer 19

I watched some of his videos where he used only rational numbers lol