This article explains how to find the intersection of 2 functions, in this case a sine function with a cosine function.

The article is based on one in English called "How to find the intersection of two functions ".

The plot will show the intersection of the functions sin(x) and cos(x) starting from an initial x value of zero. The fsolve function will be used, which returns the root of a (non-linear) equation defined by func(x) = 0.

The code is shown below:

#!/usr/bin/env python

from scipy.optimize import fsolve

#Importar pylab

import pylab

#Importar numpy

import numpy

#Se define la funcion que calcula la intercepcion

#de 2 funciones.

def EncontrarIntercepcion(fun1,fun2,x0):
    #Se usa la función lambda de la diferencia de ambas funciones con

    #valor inicial x0
    return fsolve(lambda x : fun1(x) - fun2(x),x0)

if __name__ == '__main__':

    #se calcula el resultado de la intercepcion de 2 funciones

    #sin y cos con valor inicial de 0.

    resultado = EncontrarInterseccion(numpy.sin,numpy.cos,0.0)

    #se genera el rango de -2 a 2.

    x = numpy.linspace(-2,2,50)

    #Se genera la grafica, 

    pylab.plot(x,numpy.sin(x),x,numpy.cos(x),result,numpy.sin(result),'ro')

    #se muestra la grafica.

    pylab.show()

The plot is shown below:

The sine function is in blue, the cosine plot is in green and the intersection is a red dot.

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