Something goes wrong calculating the slope of the simulation

In this python code we are trying to simulate the path of a frisbee that is being shot from a shooter with a certain angle (alpha0). The angle of attack should be the angle at which its being shot, minus the slope of its path. Thus the angle at which the air hits the frisbee. However something goes wrong here, the AoA is not 0 at the beginning, can someone help fixing our code. I suspect that the method of calculating the slope of the path is wrong.

mport numpy as np
import matplotlib.pyplot as plt

t = np.linspace(0,2,1001)
alpha0 = 26*np.pi*(1/180)
v0 = 9.0
vx0 = np.cos(np.rad2deg(alpha0))*v0
vy0 = np.sin(np.rad2deg(alpha0))*v0
x0 = 0.0
y0 = 1.0
g = -9.81
r_disc = 0.12


def Cd_frisbee(alpha):
    Cd_0 = 0.18
    Cd_alpha = 0.69
    Cd = Cd_0 + (Cd_alpha*(alpha - alpha0)**2)
    return Cd

def Cl_frisbee(alpha):
    Cl_0 = 0.33
    Cl_alpha = 1.9
    Cl = Cl_0 + (Cl_alpha*alpha)
    return Cl


def A_frisbee(alpha):
    A = np.pi*(r_disc**2)*(np.sin(alpha))
    return A

def a_Drag(Cd,A,vx):
    rho = 1.25
    m = 0.125
    ax = -0.5*(Cd*A*rho*(vx**2))/m
    return ax

def a_Lift(Cl, A, vy):
    rho = 1.25
    m = 0.125
    ay = (0.5*(Cl*A*rho*(vy**2))/m) - 9.81
    return ay

def numerical(x0, v0, a_func1, a_func2, t):
    x = np.zeros(len(t))
    y = np.zeros(len(t))
    vx = np.zeros(len(t))
    vy = np.zeros(len(t))
    ax = np.zeros(len(t))
    ay = np.zeros(len(t))
    alpha = np.zeros(len(t))
    dy = np.zeros(len(t))
    dx = np.zeros(len(t))
    vx[0] = vx0
    vy[0] = vy0
    x[0] = x0
    y[0] = y0
    ax[0] = a_func1(Cd_frisbee(alpha0), 0, vx0)
    ay[0] = a_func2(Cl_frisbee(alpha0), 0, vy0)
    alpha[0] = 0
    dy[0] = 0
    dx[0] = 0
    for i in range(len(t) - 1):
        dt = (t[i + 1] - t[i])
        x[i + 1] = x[i] + (vx[i] * dt)
        y[i + 1] = y[i] + (vy[i] * dt)
        vx[i + 1] = vx[i] + (dt * ax[i])
        vy[i + 1] = vy[i] + (dt * ay[i])
        ax[i + 1] = a_func1(Cd_frisbee(alpha[i]), A_frisbee(alpha[i]), vx[i])
        ay[i + 1] = a_func2(Cl_frisbee(alpha[i]), A_frisbee(alpha[i]), vy[i])
        dy[i+1] = (y[i + 1] - y[i])
        dx[i+1] = (x[i + 1] - x[i])
        alpha[i+1] = alpha0 - np.radians(np.arctan(dy[i+1]/dx[i+1]))
    return x, y, vx, vy, ax, ay, alpha, dy, dx


x_num = numerical(x0, v0, a_Drag, a_Lift, t)[0]
y_num = numerical(x0, v0, a_Drag, a_Lift, t)[1]
alpha_num = numerical(x0, v0, a_Drag, a_Lift, t)[6]
vx_num = numerical(x0, v0, a_Drag, a_Lift, t)[2]
dy_num = numerical(x0, v0, a_Drag, a_Lift, t)[7]
dx_num = numerical(x0, v0, a_Drag, a_Lift, t)[8]
"""
ax[0].plot(t, x_num, color='green', linestyle='--')
ax[1].plot(t, y_num, color='green', linestyle='--')
ax[3].plot(t, alpha_num, color='green', linestyle='--')
"""

I have used different starting values such as speed etc. and instead of a smooth path i got strange graphs.