c programming, this 3 are all related questions and please add comments explaining the codes thank you! :)

1. Purpose The purpose of this assignment is to write an algorithm, in the C programming language, to calculate the value of a given function f at a particular value of its argument x. The program will do this by using a McLaurin series expansion. 2. The Function of the Program Your programme should take in a value x. This will be a real variable, given to the appropriate number of decimal places. The function will return the value f(x), also a real number, to a level of accuracy managed by your program. Your function will either be given or will be the solution to a given differential equation. In the second case, you must use only the differential equation, rather than solving it and then implementing a series for the functions. 3. Method Your programme should calculate the value of f(x) based purely on the McLaurin series, without using any of the functions available in the C library. It will therefore only use the basic arithmetic operations in C; loops, addition, subtraction multiplication and division. You can use logical statements or function calls as you see fit. 5. Your assigned function The function you are asked to implement is given here: f(x) = sin(x)