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

[BC-02]

Can someone solve this equation and write the procedure?

x+cos(x)=0

Without using graph.

 

[Crosson]

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]

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

Daniel.

 

[BC-02]

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]

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.

 

[BC-02]

Thank you, I think this is sufficient for me.