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

Can someone solve this equation and write the procedure?

x+cos(x)=0

Without using graph.

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.

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

Daniel.

cos(x)=0,3 is also transcendental equation (I think), even so I can get approximate solution with my calculator (1,266 ...). Is there any possibility how to get approximate solution of x+cos(x)=0 with common calculator (for example the calculator in windows)?

Integral
Staff Emeritus
Gold Member
Express the equation as:

x = - Cos(x)

now do a fixed point iteration so

$$x_2 = - \cos (x_1)$$
and
$$x_{n +1} = - \cos (x_n)$$

Start by making a guess between 1 and 0, call this $x_1$ calculate $x_2$ ,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.

Thank you, I think this is sufficient for me.