Equation and write the procedure? x+cos(x)=0

cos(x) is a transcendental function, there isn't much point to scratching your head trying to solve a transcendental equation; it isn't likely to be expressible in terms of radicals anyway.

Use Newtons method.

 

The approximate solution is all u could get...The solution is unique,however,it is certainly a transcendental (i.e.no algebraic) number...

Daniel.

 

Express the equation as:

x = - Cos(x)

now do a fixed point iteration so

[tex] x_2 = - \cos (x_1) [/tex]
and
[tex] x_{n +1} = - \cos (x_n) [/tex]


Start by making a guess between 1 and 0, call this [itex] x_1 [/itex] calculate [itex] x_2 [/itex] ,simply repeat the process until the number stops changing. It is not incredibly fast, 20 iterations gets you around 3 digits. Keep iterating until you are tired of pushing buttons, observe the digits that do not change. The unchanging digits are your answer. If you want more digits iterate some more.