4. (20 points) Find the approximate value of c such that if we pick zo [-c, c) the Newton's Method for finding the root of f(1) = sin x is guaranteed to converge to the root a = 0. Show your work reasoning and method through with you arrive at such a value c. For full credit, your method to arrive at c must be as efficient as possible. (Hint: Think of the graph for the function sinr and consider the tangent to this sine curve at c.) 4. (20 points) Find the approximate value of c such that if we pick zo [-c, c) the Newton's Method for finding the root of f(1) = sin x is guaranteed to converge to the root a = 0. Show your work reasoning and method through with you arrive at such a value c. For full credit, your method to arrive at c must be as efficient as possible. (Hint: Think of the graph for the function sinr and consider the tangent to this sine curve at c.)