1. Newton's Method - Trig Function

Is it possible to find the value of trig roots through Newton's method?
(Such as cos 4.49...)

2. Originally Posted by Lord Voldemort
I was doing a problem in the Newton's method section, and after a while, it came out to evaluate cosine 4.493409. I can't figure out how to use Newton's method here. Is it even possible? I've already used Newton's method once in order to get to this value, so I'm thinking I can just leave it in exact terms. Any ideas?
Hello He who shall not be named. Please post the original problem as it is written in the text. Your post lacks clarity.

3. Sorry - Original Question:
Of the many lines that are tangent to y = - sin x and pass through (0,0), one has the largest slope. Use Newton's method to find the slope of that line correct to six decimal places. Using Newton's method, I found that the slope of the line would be cosine (4.493409). My question is - is there any possible way to find the value of cosine (4.493409) using Newton's method, or can should I just find the value with my calculator?