x-sinx=a

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The equation x - sin x = a has to be solved for x. x is in radians and a is a constant.

x - sin x = a

=> x - a = sin x

The plot of sin x is :

As the true value of x is not known, it is not possible to plot the graph of x - a. If the graph is plotted with the graph of sin x, the x-coordinate of the point of contact of the two graphs is the solution of the equation x - sin x = a.

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aruv | High School Teacher | (Level 2) Valedictorian

Posted on

It is an equation in two variables namely x and a. It may have infinite number of solutions.

`x-sin(x)=a`

`` Let

x=a                     (i)

then

`sin(a)=0`

`a=npi` where n is an integer.

Thus

`x=a=npi`

Let `x!=a` , then define

`f(x)=x-sin(x)-a`

Let plot graph and find zero of f(x) for different values of a which in turn be the solution of the given equation.

`a=0,+-1,+-2,+-3,+-4,+-sqrt(2),x,.....`

Except blue graph when x=a , f(x) has unique solution. For different value of a, we have different solution.

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