Sin(x) Formula

The following formula of mine is a rediscovery of the standard taylor series for the sin function. I thought to note this because of its impact on my mathematical development as an individual.

At first I had only discovered the Taylor Series of sin(1) that being (down below on the right side) where x=1 while recalling the Madhava-Leibniz series and then asking myself what would happen if I added factorials. To my utter shock and amazement the series seemed to be tending(when summed to n terms) to sin(1) (The Madhava-Leibniz series is simply the same series as sin(1) without the factorials in its denominator)

Latter, I revisited the Madhava-Leibniz series article in Wikipedia. There it states that the Madhava-Leibniz series is just a subsequence of the inverse tangent function with x=1. I then looked at the series of the inverse tangent function(Same series as Sin(x) without factorials in the denominator) and saw that if I added factorials to the denominators of the terms of this series, I would get the sin(x) series! In retrospect, all I had was a computer with the Madhava-Leibniz series article pulled up, a calculator, and a over curious mind.

See Madhava-Leibniz series article on Wikipedia-https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80

Interestingly a nice approximation for Pi (accurate to six digits) is 11^ln(11) *10^-2 curiously enough.

Thank you,

Nunghead