The problem was split into three parts. First part is creating two variables with a length of 100 and then print their shape.

import numpy as np

X_n = np.array(range(100))
Y_n = np.array(range(100))

print(X_n.shape)
print(Y_n.shape)

Next it was defining two functions f_x and f_y for the following equations and an added rule that it should include the parameter r, number n for numbering the points, and the previous coordinate x_n or y_n. The functions

fx(x_n) = x_n - ((2*pi)/100) * sin*((2*pi*n)/100) *r

fy(y_n) = y_n + ((2*pi)/100) * cos*((2*pi*n)/100) *r

import numpy as np

def f_x(r, n, x_n):
    '''Compute the x-coordinate x_(n+1) from x_n'''

    return x_n - ((2*np.pi)/100)*np.sin((2*np.pi*n)/100) * r


import numpy as np

def f_y(r, n, y_n):
    '''Compute the y-coordinate y_(n+1) from y_n'''

    return y_n + ((2*np.pi)/100)*np.cos((2*np.pi*n)/100) * r

These were autocorrected and were correct.
The last part was determining the first 100 coordinates and saving them in X_n and Y_n using our work from the previous problems. r =6/4.

So this is what I have, and it's apparently wrong. I am absolutely losing my shit over it because I have no idea what I'm doing wrong and I have so much other stuff to study.

import numpy as np

# Create numpy arrays to save computed points
X_n = np.array(range(100), dtype=float)
Y_n = np.array(range(100), dtype=float)

# Set parameter r
r = 6 / 4

# Define functions to compute the coordinates
def f_x(r, n, x_n):
    return x_n - ((2*np.pi)/100)*np.sin((2*np.pi*n)/100) * r


def f_y(r, n, y_n):
    return y_n + ((2*np.pi)/100)*np.cos((2*np.pi*n)/100) * r

# Compute the coordinates
for n in range(99):
    X_n[n+1] = f_x(r, n, X_n[n])
    Y_n[n+1] = f_y(r, n, Y_n[n])
#round to three decimals
print(round(X_n[0], 3), round(X_n[25], 3), round(X_n[50], 3), round(X_n[75], 3))
print(round(Y_n[0], 3), round(Y_n[25], 3), round(Y_n[50], 3), round(Y_n[75], 3))