Python: estimate Pi with trig functions as efficiently as possible

Question

I have an assignment where I need to approximate Pi in a computationally efficient manner. Here is my strategy: I use a unit circle, the angle bisector of an isoceles triangle, and the definition of sin. I drew a diagram:

For example, if I want to use an hexagon (6 points/6 sides), I simply need to compute a:(0.5*sin(2*pi/2*x) and multiply it by (2*x). Finally, since Pi = Circumference/Diameter, then my approximation of Pi = polygon perimeter (since Diameter = 1).

Essentially:

from math import sin, pi
def computePi(x):    #x: number of points desired
    p = x*sin(pi/x)
    print(p)

computePi(10000)
3.141592601912665

It works, and I think it's as efficient as it gets, no? Thank you for your time!

EDIT: to avoid circularity, I redid it using Archimedes algorithm using only the Pythagorean theroem:

Code:

from math import sqrt

def approxPi(x):                  #x: number of times you want to recursively apply Archmidedes' algorithm
    s = 1                         #Unit circle
    a = None; b = None;   
    for i in range(x):
        a = sqrt(1 - (s/2)**2)
        b = 1 - a
        print('The approximate value of Pi using a {:5g}-sided polygon is {:1.8f}'.format(6*2**(i),(s*6*2**(i))/2))
        s = sqrt(b**2 + (s/2)**2)

Answer 1

Even better is

print(4 * math.atan(1))

This does not use pi in any obvious way in the calculation (though as @Jean-FrançoisFabre comments, pi is probably used in the function definition), and in addition to the trig function it has just one simple multiplication. Of course, there is also

print(2 * math.acos(0))

and

print(2 * math.asin(1))