I Error estimate for iterative convergence

[member 428835]

On the following page on wikipedia:

https://en.wikipedia.org/wiki/Fixed-point_iteration

the section "Examples" has a second bullet point, where the author suggests $q=0.85$, but how did they get this number? I tried googling everything and could not find out how $q$ is determined.

 

[mathman]

Guess $sin(1)\approx .85$.

 

[member 428835]

Guess $sin(1)\approx .85$.

Why $\sin 1$?

 

[mathman]

Why $\sin 1$?

It is guess based only on $cos(1)$ being in the original question.

 

[member 428835]

It is guess based only on $cos(1)$ being in the original question.

But $\cos(1) = 0.54 \neq 0.85$, so where is the 0.85 coming from? Asked differently, where did you get the $\sin$ from?

 

[mathman]

But $\cos(1) = 0.54 \neq 0.85$, so where is the 0.85 coming from? Asked differently, where did you get the $\sin$ from?

sin(1)=.85. My guess was that it more than just a coincidence.