# -----------------------------------------------------------------------------
# Copyright (c) 2015, Nicolas P. Rougier. All Rights Reserved.
# Distributed under the (new) BSD License. See LICENSE.txt for more info.
# -----------------------------------------------------------------------------
import numpy as np
import matplotlib.pyplot as plt

plt.figure(figsize=(8,5), dpi=80)
ax = plt.subplot(111)
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.spines['bottom'].set_position(('data',0))
ax.yaxis.set_ticks_position('left')
ax.spines['left'].set_position(('data',0))

X = np.linspace(-np.pi, np.pi, 256,endpoint=True)
C,S = np.cos(X), np.sin(X)

plt.plot(X, C, color="blue", linewidth=2.5, linestyle="-", label="cosine")
plt.plot(X, S, color="red", linewidth=2.5, linestyle="-",  label="sine")

plt.xlim(X.min()*1.1, X.max()*1.1)
plt.xticks([-np.pi, -np.pi/2, 0, np.pi/2, np.pi],
           [r'$-\pi$', r'$-\pi/2$', r'$0$', r'$+\pi/2$', r'$+\pi$'])

plt.ylim(C.min()*1.1,C.max()*1.1)
plt.yticks([-1, +1],
           [r'$-1$', r'$+1$'])

t = 2*np.pi/3
plt.plot([t,t],[0,np.cos(t)],
         color ='blue',  linewidth=1.5, linestyle="--")
plt.scatter([t,],[np.cos(t),], 50, color ='blue')
plt.annotate(r'$\cos(\frac{2\pi}{3})=-\frac{1}{2}$',
             xy=(t, np.cos(t)),  xycoords='data',
             xytext=(-90, -50), textcoords='offset points', fontsize=16,
             arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.2"))

plt.plot([t,t],[0,np.sin(t)],
         color ='red',  linewidth=1.5, linestyle="--")
plt.scatter([t,],[np.sin(t),], 50, color ='red')
plt.annotate(r'$\sin(\frac{2\pi}{3})=\frac{\sqrt{3}}{2}$',
             xy=(t, np.sin(t)),  xycoords='data',
             xytext=(+10, +30), textcoords='offset points', fontsize=16,
             arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.2"))

plt.legend(loc='upper left', frameon=False)
plt.savefig("../figures/exercice_9.png",dpi=72)
plt.show()