# How were trigonometrical functions and its inverses discovered?

Imagine you just did a circle. Some functions are just definitions, like $\sin$,$\cos$ and $\tan$ but how do you derive a formula to get the $\sin$ from an angle in radians (maybe by Taylor series, but then you should know that $(\sin(x))'=\cos(x)$)? Or a formula to get the original angle from its $\sin$?

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Maybe somebody got an angle from the original $\sin$ a long time ago:-) –  Marc van Leeuwen Mar 17 '13 at 11:44
–  user32847 Mar 17 '13 at 12:08
@Brainstorming: Nice link! –  dot dot Mar 17 '13 at 12:09