1) Consider a function f(x) = cos(x), whose values monotonically decrease from 1 (when x = 0 degrees) to -1 (when x = 180 degrees) in the range of [0...180] for the angle (in degrees). Your task for this question is to come up with a binary search algorithm to determine the largest value of 'x' ('referred to as the threshold value for x) for which f(x) is greater than a target 't'. The target 't' value can be anywhere in the interval/range (-1, ..., 1). Note that this is a open interval, so the 't' value will be greater than -1, but less than 1. Termination condition: Run the iterations until the difference between the right index and left index is greater than 0.1.

(a) Choose the appropriate initial values for the left index (LI) and right index (RI).

(b) State the invariant property that will be maintained for the LI and RI vis-a-vis the f(x) values for the entire algorithm.

(c) Provide a pseudo code of the binary search algorithm, including the scenarios when you will move the LI and RI (d) Run the algorithm of

(c) for the target 't' value of 0.25 and show the details (LI, RI, middle index: MI and f(MI) values as well as how the LI or RI are adjusted for each iteration) until the termination. (e) What is the theoretically expected number of iterations based on the initial values for LI and RI as well as the termination condition? How does this compare to the number of iterations observed in (d)? You will get a ZERO if you just use a brute force approach