Computing the fixed point for cosx While studying about Compiler Design I came with the term 'fixed point'.I looked in wikipedia and got the definition of fixed point but couldn't get how fixed point is computed for cosx as said in fixed point.it says that the fixed point for cosx=x using Intermediate Value Theorem.But I couldn't get how they computed the fixed point for cosx.Do anyone know how they computed this?

alexmjn

alexmjn

Answered question

2022-09-01

Computing the fixed point for cos x
While studying about Compiler Design I came with the term 'fixed point'.I looked in wikipedia and got the definition of fixed point but couldn't get how fixed point is computed for cos x as said in fixed point.
It says that the fixed point for cos x=x using Intermediate Value Theorem.But I couldn't get how they computed the fixed point for cos x.Do anyone know how they computed this?

Answer & Explanation

Carleigh Tate

Carleigh Tate

Beginner2022-09-02Added 8 answers

You have an equation as:
x = cos x
We can write this as an iteration formula:
x n + 1 = cos x n
We would choose a starting value and iterate it:
x 0 = 0.75
x 1 = cos x 0 = cos ( 0.75 ) = 0.731689
x 2 = cos x 1 = cos ( 0.731689 ) = 0.744047
...
We arrive at a repeating sequence with x = 0.739085
We would of course do this to whatever precision we needed (if the fixed point exists).
Check
Claim is that x = cos x
cos ( 0.739085 ) = 0.739085

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