import numpy as np
import matplotlib.pyplot as plt

def descartes(ax, ran_x, ran_y, ax_title,x_label = "x", y_label = "y"):
    ax.set_xlabel(x_label, fontsize = 12)
    ax.set_ylabel(y_label, fontsize = 12)
    ax.set_xlim(ran_x[0], ran_x[1])
    ax.set_ylim(ran_y[0], ran_y[1])
    ax.set_title(ax_title, fontsize = 14)
    ax.grid()
    ax.axhline(0, color = "black")
    ax.axvline(0, color = "black")

fig = plt.figure(figsize = (5, 5))
ax = fig.add_subplot(111)

title1 = "Tokyo University 2023 Math qu.1 NO1"
cnt1=10
descartes(ax, [0,cnt1*np.pi], [0, 3],title1)

t=np.linspace(np.pi,cnt1*np.pi,1000)
y=abs(np.sin(t))/2*np.sqrt(t)
ax.plot(t ,y , color = "red")

for k in range(1,cnt1):
    t=np.linspace(k*np.pi,(k+1)*np.pi,1000)
    y=abs(np.sin(t))/2*np.sqrt(k*np.pi)
    ax.plot(t ,y , color = "blue")

    t=np.linspace(k*np.pi,(k+1)*np.pi,1000)
    y=abs(np.sin(t))/2*np.sqrt((k+1)*np.pi)
    ax.plot(t ,y , color = "green")

plt.show()