# When did mathematicians invent the unit circle to extend the trig functions?

Is there any evidence showing that a unit circle approach was used by early mathematicians?

• Could you please explain a little more what you mean? – kimchi lover Jan 17 '20 at 1:36
• At what period of time was the concept of the 'unit circle' invented or created. Was it back in the Roman era? During Isac Newton's time? Do we know a specific date in which it was created or do we not know at all? That's what I'm trying to say. – Dom Turner Jan 17 '20 at 2:24
• The problem with very old history is that it is hard to find out the truth. Indians claim they invented these, and then Arabs took it forward, as if they were mere translators of Greek and Indian science. Finally, Europeans learned from the translations of Arabic works. There is so much historical bias, depending on who wrote the history and in which part of the world. The lack of original works, and extensive nationalistic nonsense out there will never make it possible to find out the truth. – M. Farooq Jan 17 '20 at 4:15
• The science history around the 17th-18th century is reliable enough but before that take everything with a grain of salt. – M. Farooq Jan 17 '20 at 4:17
• oh ok, so I guess there just isn't enough evidence to precisely or at least reasonably predict who and when created the concept of the unit circle. – Dom Turner Jan 17 '20 at 5:58

He then denotes half of the circumference by the familiar $$\pi$$, and gives the standard suite of trig identities.
• Huh? How did Euler know $2 \pi$ is irrational? – vonbrand Feb 6 '20 at 22:32