import numpy as np
import matplotlib.pyplot as plt
import scipy.optimize as opt

#prvi zadatak
def f1(x):
    return np.sin(x)
def f2(x):
    return np.cos(x)
x = np.linspace(0,20,100)
plt.plot(x,f1(x),'g',label = 'f1')
plt.plot(x,f2(x),'r',label = 'f2')
plt.legend()


#drugi zadatak
def f(x):
    return f2(x) - f1(x)
n = []
for i in range(3): #jer moramo 3 sjecista odrediti
        n.append(fsolve(f, 3*i)[-1])
n = np.array(list(set(n)))
plt.scatter(n, f1(n), marker = 'o', color = 'red')

#treci zadatak
plt.fill_between(x, f1(x), color = 'lightblue')

#cetvrti zadatak
p1 = np.trapz(f1(x), x, dx = 0.2)
p2 = np.trapz(f2(x), x, dx = 0.2)
print(p2-p1) #kada se trazi samo razlika ne treba na abs


#peti zadatak
def difj(z,t):
    return 3.2*z*np.sin(np.sqrt(z))
t = np.linspace(0,10,100)
z = odeint(difj, [10,-1], t)
plt.figure()
plt.plot(t,z)

plt.show()