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?