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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