# Math Help - Newton's method

1. ## Newton's method

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

2. Originally Posted by tbenne3
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
$f(x) = x - \cos{x}$

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

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

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