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

  • Thread starter BC-02
  • Start date
  • #1
3
0
Can someone solve this equation and write the procedure?

x+cos(x)=0

Without using graph.
 

Answers and Replies

  • #2
1,250
2
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.
 
  • #3
dextercioby
Science Advisor
Homework Helper
Insights Author
13,017
566
The approximate solution is all u could get...The solution is unique,however,it is certainly a transcendental (i.e.no algebraic) number...

Daniel.
 
  • #4
3
0
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)?
 
  • #5
Integral
Staff Emeritus
Science Advisor
Gold Member
7,201
56
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.
 
  • #6
3
0
Thank you, I think this is sufficient for me.
 

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

Replies
4
Views
2K
Replies
2
Views
646
Replies
6
Views
2K
Replies
10
Views
1K
Replies
4
Views
5K
Replies
7
Views
909
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
1
Views
2K
Top