SOLUTION: Find the real root of the transcedental equation cos x - 3x + 1 = 0 correct to four decimal places using iteration method.

Question 696991: Find the real root of the transcedental equation cos x - 3x + 1 = 0 correct to four decimal places using iteration method.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
NOTE: In math, when we see , we assume is measured in radians, not degrees.

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We know that the graphs of and look like this:

We need to look for the point where they intersect.

At , is greater than ,

,
but at , is lesser than ,

,
so the answer is between and .
For , is greater than , with

,
but they are very close, much closer that at ,
so the answer is between and ,
but we expect it to be close to .
For , is lesser than , with

,
so the answer is between and .
We may try ,
where is still a bit too high,
and then try , getting

,
where is still a bit too high,
but very, very close.
We could next try , getting

,
where is still a hair too high.
We can then try , getting

,
where is a bit too low.
That tells us that the answer is between and .
We seemed to be closer at , so maybe we should try .
For , is also a bit too low, with

and ,
both of which round to .
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