1. The function sin(x) can be approximated by summing the first n terms of the infinite...

 

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1. The function sin(x) can be approximated by summing the first n terms of the infinite series sin(x)=x-x/3! + x/5! - x/7! + ... where x is expressed in radians (Note: radians = 180). Write a C program that can be used to answer the following questions during the lab: a) For a value of x = 0.1, how many terms do you need in the power series so that the result from the series equals the result from the sin(x) library function up to the 6 decimal place. b) For a value of x = 1.3, how many terms do you need for achieving the same accuracy as in (a)? Assume that there exists a function double fact(int n) that returns the factorial value of an integer as a double. This function will be given to you. There is a standard C function double pow(double x, double y) that returns the result of x to the power y as a double type. You will need to include math.h to use this function (#include ). 1. The function sin(x) can be approximated by summing the first n terms of the infinite series sin(x)=x-x/3! + x/5! - x/7! + ... where x is expressed in radians (Note: radians = 180). Write a C program that can be used to answer the following questions during the lab: a) For a value of x = 0.1, how many terms do you need in the power series so that the result from the series equals the result from the sin(x) library function up to the 6 decimal place. b) For a value of x = 1.3, how many terms do you need for achieving the same accuracy as in (a)? Assume that there exists a function double fact(int n) that returns the factorial value of an integer as a double. This function will be given to you. There is a standard C function double pow(double x, double y) that returns the result of x to the power y as a double type. You will need to include math.h to use this function (#include ).