#%%
# Numpy initialisieren
import numpy as np
import matplotlib.pyplot as plt
#%%
print("Aufgabe 2")
print(f"a) {1/3}")
print(f"b) {2/3}")
print(f"c) {1/7}")
print(f"d) {1-0.9999}")
print(f"e) {1-0.999999999999}")
print(f"f) {((1/2) - np.sin(np.pi/6)) ** (1/4)}")

#%%
print("Aufgabe 6")
print(f"a) {np.power(np.array([45.6]), 3)}")
print(f"b) {np.sqrt(3)}")
print(f"c) {np.power(np.array([2]), (1/5))}")
print(f"d) {np.power(np.array([5.654 * np.power(np.array([10]), 24)]), (1/7))}")
print(f"e) {np.power(np.array([44.5]), (5/9))}")
print(f"f) {4 * np.pi}")
print(f"g) {np.sin(5 * np.pi / 4)}")
print(f"h) {1 / np.tan(-3 * np.pi / 5)}")
print(f"i) {np.tan(np.radians(77))}")
print(f"j) {np.arccos(-0.45)}")
print(f"k) {1 / np.arctan(34.1)}")
print(f"l) {np.power(np.array([np.e]), -3.34)}")
print(f"m) {np.e}")
print(f"n) {np.log(13.2)}")
print(f"o) {np.log10(23)}")
print(f"p) {np.log2(69.6)}")

# %%
print("Aufgabe 7")
# Parameter
a = 12.3, b = 8.14, pr = 3, ME = "cm"

# Berechnungen
c = np.sqrt(a**2+b**2)

# Ausgabe
print("----------------------------------------------------------------------")
print(__file__)
print("----------------------------------------------------------------------")
print(f"Seite a = {a:#.{pr}g} {ME}")
print(f"Seite b = {b:#.{pr}g} {ME}")
print(f"Seite c = {c:#.{pr}g} {ME}")
print("----------------------------------------------------------------------")

# %%
print("Aufgabe 7.d)")
# Parameter
a = 0.85e3; pr_a = 2;   sc_a = 1.0e-3;  ME_a = "km";\
b = 234;    pr_b = 3;   sc_b = 1.0;     ME_b = "m";\
            pr_c = 2;   sc_c = 1.0e-3;  ME_c = "km";\

# Berechnungen
c = np.sqrt(a**2+b**2)

# Ausgabe
print("----------------------------------------------------------------------")
print(__file__)
print("----------------------------------------------------------------------")
print(f"Seite a = {a*sc_a:#.{pr_a}g} {ME_a}")
print(f"Seite b = {b*sc_b:#.{pr_b}g} {ME_b}")
print(f"Seite c = {c*sc_c:#.{pr_c}g} {ME_c}")
print("----------------------------------------------------------------------")

# %%
print("Aufgabe 8")
# Python konfigurieren
plt.close("all")
plt.rcParams["figure.figsize"] = (7.03,15)
plt.rcParams["font.size"] = 9
plt.rcParams["font.family"] = "serif"
plt.rcParams["text.usetex"] = False

# Parameter
x_0 = 0
x_E = 4
N = 201
lw = 3
fig = 1

# Funktionen
def f(x):
    y = 3/(1+x)
    return y

def g(x):
    y = x/2
    return y

# Daten
x_data = np.linspace(x_0, x_E, N)
f_data = f(x_data)
g_data = g(x_data)

# pltot
fh = plt.figure(fig)
plt.plot(x_data, f_data, linewidth = lw, label = r"$f$")
plt.plot(x_data, g_data, "--", linewidth = lw, label = r"$g$")
plt.xlabel(r"$x$")
plt.ylabel(r"$y$")
plt.legend()
plt.grid(visible=True)
plt.axis("image")