Newton's method

Feb 2010
98
0
I got this problem wrong on my test and I am currently studying for my final so I was seeing if someone could show me a step by step on how to do this problem. I understand Newton's method when dealing with easier numbers/no trig, but I can't get this one.


Use Newton's method to approximate the root of the equation cosx=x. Choose x1 = 1, Find x2. The answer = 0.75
 

skeeter

MHF Helper
Jun 2008
16,216
6,764
North Texas
I got this problem wrong on my test and I am currently studying for my final so I was seeing if someone could show me a step by step on how to do this problem. I understand Newton's method when dealing with easier numbers/no trig, but I can't get this one.


Use Newton's method to approximate the root of the equation cosx=x. Choose x1 = 1, Find x2. The answer = 0.75
\(\displaystyle f(x) = x - \cos{x}\)

\(\displaystyle f'(x) = 1 + \sin{x}
\)

\(\displaystyle x_2 = x_1 - \frac{f(x_1)}{f'(x_1)}\)

\(\displaystyle x_2 = 1 - \frac{1 - \cos(1)}{1 + \sin(1)} \approx 0.75036...
\)
 
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