Friday, February 21, 2014

Sine and Cosine Graph using Python

Sine and Cosine Graph

Introduction to Sine/Cosine Graph

The sine and cosine graphs are almost identical, except the cosine curve (y = cos(x)) starts at amplitude y = 1, when angle x = 0° (whereas the sine curve (y = sin(x)) starts at amplitude y = 0). We say the cosine curve is a sine curve which is shifted to the left by 90°. The graph of sine and cosine is like a wave that forever oscillates between -1 and 1, in a shape that repeats itself every 360° (2π) units.

Program Implementation

In this tutorial, I have used Python 3.5.2 (64-bit) software, and 7 modules: MatPlotLib 2.0.2, PyParsing 2.2.0, Python-DateUtil 2.6.1, PyTZ 2017.2, SetupTools 36.2.0, Cycler 0.10.0, and NumPy-MKL 1.13.1 implemented in Windows 10 Enterprise operating system. The 7 modules are chosen based on the compatibility of Python and OS version and bit.

Source Code

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, color = "blue", linewidth = 1,
           linestyle = "-", label = r'$y = cos(x)$')
plt.plot(X, S, color = "red", linewidth = 1, 
           linestyle = "-",  label = r'$y = sin(x)$')
plt.legend(loc = 'upper left')

ax = plt.gca()
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.yaxis.set_ticks_position('left')
ax.xaxis.set_ticks_position('bottom')
ax.spines['left'].set_position(('data', 0))
ax.spines['bottom'].set_position(('data', 0))

plt.xlim(X.min() * 1.1, X.max() * 1.1)
plt.xticks([-np.pi, -np.pi / 2, 0, np.pi / 2, np.pi],
           [r'$-180^\circ$', r'$-90^\circ$', r'$0$', r'$+90^\circ$', r'$+180^\circ$'])

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

plt.show()


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