4. In addition to the 'cos' pre-defined function, which is found in the 'cmath' library, the cosine of an angle 'x' (given in radians), can be estimated using the following infinite series: x* +...

Extracted text: 4. In addition to the 'cos' pre-defined function, which is found in the 'cmath' library, the cosine of an angle 'x' (given in radians), can be estimated using the following infinite series: x* + +..+(-1)" 2! 4! cos(x) =1- +... (2n)! However, based on the number of terms 'n' used in the above series, an ERROR MARGIN (EM) can be found between the estimated value and the value returned by the pre-defined function 'cos'. Write a C++ program, which does the following: 1. Allows the user to enter the value of the EM, which must be between 0 and 0.0010. A suitable error message should be displayed if EM is entered outside this range and the program must terminate 2. Reads a list of angles (given in degree) from a text file (see angles.txt). The program should only accept angles between 0 and 180°. When invalid angle is read from the file, an error message should be displayed (see the sample output) 3. Includes THREE user-defined functions to perform the following tasks: a. Convert the angle from degree to radians using: radians = degree x b. Compute the n! to be used in the above series c. Compute the estimated cosine as given by the above series 4. Counts the number of terms 'n’ used in the above series to satisfy the provided EM 5. Formats the output as shown below (Use 8 decimal places for all real numbers)| 180°


Extracted text: C. C:\Windows\system32\cmd.exe Enter the ERROR margin (bet 0 and 0.0010): 0.0500 ***Invalid ERROR MAŘGIN limit. Program ends...*** Press any key to continue angles.txt 100 C:\Windows\system32\cmd.exe 25 33 Enter the ERROR margin (bet 0 and 0.0010): 0.001 190 cos(x) estimated #of terms 50 86 100 -0.17277674 -0.17270646 0.90640125 0.90641077 5 3 25 5 33 0.83882956 0.83887981 -20 190 **ang le is out of range** 50 0.64312645 0.64372976 170 86 0.07051553 0.06989479 0.99619855 0.99619614 13 -20 170 -0.98454544 -0.98546634 **angle is out of range** 45 13 0.97439593 0.97428592 45 0.70738827 0.70770972 Press any key to continue 342 623