I have been trying to calculate pi using the formula.
$$n \sin\bigg(\frac{180}{n}\bigg) \cos\bigg(\frac{180}{n}\bigg)$$
This formula is a simplified regular polygon area formula, without being multiplied by the radius squared. The basis for it calculating pi is that as a circle is effectively a regular polygon with an infinite number of sides, they also have an area of pi when having a radius of 1. As you get larger and larger numbers of sides the area of the regular polygon matches more and more of pi. The problem I'm having is that all of the $\sin/\cos$ functions on the internet use radians, I can't do that if I want to calculate pi sadly. But, I had an idea, the top half of the unit circle can be graphed with the following, $Y = \sqrt{1 - x^2}.$ I could then calculate the intercept between this and the $\sin/\cos$ line with the slope of the angle. My problem so far has been getting the slopes to make coherent angles to me. For instance, when I do this with, $Y = x$, I get the same answer as $\sin(45^\circ)$. However, if I want to do $22.5$ degrees, it ends up just shy of $Y = .4X$, not $Y = .5X$, as I initially assumed. So, ultimately I'm wondering if there is a way to find the angle of a line against the $X$-Axis without using trig functions if you know the slope. Also, it doesn’t have to work above 45 degrees as it is unlikely I will ever use these $\sin/\cos$ functions for any other purpose.