from pylab import *

figure(figsize=(8,5), dpi=80)
subplot(111)

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

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

ax = 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))

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

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


legend(loc='upper left')

t = 2*np.pi/3
plot([t,t],[0,np.cos(t)],
     color ='blue',  linewidth=1.5, linestyle="--")
scatter([t,],[np.cos(t),], 50, color ='blue')
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"))

plot([t,t],[0,np.sin(t)],
          color ='red',  linewidth=1.5, linestyle="--")
scatter([t,],[np.sin(t),], 50, color ='red')
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"))

for label in ax.get_xticklabels() + ax.get_yticklabels():
    label.set_fontsize(16)
    label.set_bbox(dict(facecolor='white', edgecolor='None', alpha=0.65 ))


savefig("figure-4-right.pdf")
show()
