Please write C++ programe 4. In addition to the 'cos' pre-defined function, which is found in the 'cmath' library, thecosine 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-definedfunction '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. Asuitable error message should be displayed if EM is entered outside this range and theprogram must terminate2. Reads a list of angles (given in degree) from a text file (see angles.txt). The programshould only accept angles between 0 and 180°. When invalid angle is read from thefile, 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 xb. Compute the n! to be used in the above seriesc. Compute the estimated cosine as given by the above series4. Counts the number of terms 'n’ used in the above series to satisfy the provided EM5. Formats the output as shown below (Use 8 decimal places for all real numbers)|180° C. C:\Windows\system32\cmd.exeEnter the ERROR margin (bet 0 and 0.0010): 0.0500***Invalid ERROR MAŘGIN limit. Program ends...***Press any key to continueangles.txt100C:\Windows\system32\cmd.exe2533Enter the ERROR margin (bet 0 and 0.0010): 0.001190cos(x)estimated #of terms5086100 -0.17277674 -0.172706460.90640125 0.9064107753255330.83882956 0.83887981-20190 **ang le is out of range**500.64312645 0.64372976170860.07051553 0.069894790.99619855 0.9961961413-20170 -0.98454544 -0.98546634**angle is out of range**45130.97439593 0.97428592450.70738827 0.70770972Press any key to continue342623

The question is on writing the C++ code considering the given criteria.

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? x* cos(x) = 1- +- +...+(-1)"- 2! 4! +. (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

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? x* cos(x) = 1- +- +...+(-1)"- 2! 4! +. (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

C++ for Engineers and Scientists

4th Edition

ISBN:9781133187844

Author:Bronson, Gary J.

Publisher:Bronson, Gary J.

Chapter6: Modularity Using Functions

Section6.4: A Case Study: Rectangular To Polar Coordinate Conversion

Problem 9E: (Numerical) Write a program that tests the effectiveness of the rand() library function. Start by...

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