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import numpy as np

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

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import numpy as np
import matplotlib.pyplot as plt

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

plt.plot(X,C)
plt.plot(X,S)

plt.show()

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# Imports
import numpy as np
import matplotlib.pyplot as plt

# Create a new figure of size 8x6 points, using 100 dots per inch
plt.figure(figsize=(8,6), dpi=80)

# Create a new subplot from a grid of 1x1
plt.subplot(111)

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

# Plot cosine using blue color with a continuous line of width 1 (pixels)
plt.plot(X, C, color="blue", linewidth=1.0, linestyle="-")

# Plot sine using green color with a continuous line of width 1 (pixels)
plt.plot(X, S, color="green", linewidth=1.0, linestyle="-")

# Set x limits
plt.xlim(-4.0,4.0)

# Set x ticks
plt.xticks(np.linspace(-4,4,9,endpoint=True))

# Set y limits
plt.ylim(-1.0,1.0)

# Set y ticks
plt.yticks(np.linspace(-1,1,5,endpoint=True))

# Save figure using 72 dots per inch
# savefig("../figures/exercice_2.png",dpi=72)

# Show result on screen
plt.show()

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plt.figure(figsize=(10,6), dpi=80)
plt.plot(X, C, color="blue", linewidth=2.5, linestyle="-")
plt.plot(X, S, color="red",  linewidth=2.5, linestyle="-")

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plt.xlim(X.min()*1.1, X.max()*1.1)
plt.ylim(C.min()*1.1, C.max()*1.1)

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plt.xticks( [-np.pi, -np.pi/2, 0, np.pi/2, np.pi])
plt.yticks([-1, 0, +1])

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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.yticks([-1, 0, +1],[r'$-1$', r'$0$', r'$+1$'])

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ax = plt.gca()
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))

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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.legend(loc='upper left', frameon=False)

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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'$\sin(\frac{2\pi}{3})=\frac{\sqrt{3}}{2}$',
             xy=(t, np.sin(t)), xycoords='data',
             xytext=(+10, +30), textcoords='offset points', fontsize=16,
             arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.2"))

plt.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'$\cos(\frac{2\pi}{3})=-\frac{1}{2}$',
             xy=(t, np.cos(t)), xycoords='data',
             xytext=(-90, -50), textcoords='offset points', fontsize=16,
             arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=.2"))