Problem 3. (20 pls) Consider the roots of the equation sin x 1: cos x = 0 a) (5 pts) Write Newton's method for computing x'k'\") from the previous value x0\") for this problem. b) {5 pts) Simplify your result for large I\"). e) (10 pts} Assume you have computed root 1,} of this equation for some large value of at using Newton's method. Use the result from part (b) to explain why 2:521 = x; + It is a good guess for the next root when using Newton's method. You may (or may not) find the following trigonometric identities useful. sin(a + b) = sin a cosh + cosasinb 050.: + b) = cos acosb - sin a sin b