Newtons method, sinx=1 find solution to 8 decimal places

Question

Let sinx=1-x, use newtons method to find the solution accurate to 8 decimal places. Show initial guess, iteration equation, and all intermediate values prior to final answer?

Answer 1

Newton's Method works best in this case when you choose a value that will yield a number very close to the zero. 0.510973429 is the approximate zero. I used 0.511 as an initial guess and used x_n-(sin(x_n)+x_n-1)/(cos(x_n)+1) for the iterations.

Try a number such as zero and stick with the iterations (MS Excel or Google Sheets works well) to see what you get. Graphing it with a graphing calculator can also help explain what's going on with the iterations.

Depending upon your initial guess, Newton's Method may not work too well for you unless you interpret the output & adjust accordingly.