# Import of packages:

import numpy as np
import matplotlib.pyplot as plt

# Def of objective function:

def fun_f(x, params):
    L = params[0]
    D = params[1]
    x_rad = x*np.pi/180
    V = (D*L**2*np.cos(x_rad)*np.sin(x_rad))
    f = -V
    return f

# Model params:
    
L = 4  # [m]    
D = 5  # [m]
params = [L, D]

# Defining value range of optim variable:

x_lb = 0  # [deg]
x_ub = 90  # [deg]
N_x = 1000
x_array = np.linspace(x_lb, x_ub, N_x)

# Initialization:

f_min = np.inf 
x_opt = 0  # Strictly not necessary to define here

# Grid method of optimization:

for x in x_array:
    f = fun_f(x, params)
    if (f < f_min):  # Improvement of solution
        f_min = f  # Updating objective function
        x_opt = x  # Updating optimal solution

V_max = -f_min

# Presenting results:

print('x_opt =', f'{x_opt:.1f}')
print('f_min =', f'{f_min:.1f}')
print('V_max =', f'{V_max:.1f}')