Question

The mathematician Euler proved that: tan-(x) = x -. Write a C program to do the following: -Ask user to enter the value of (x) radians, -0.5<=x<=0.5. -Calculate and print the actual value atan (x)in degrees. - Use loops to calculate and print the series sum in degrees. -loop should stop when absolute difference between actual and series sum become <=10-3. -Print out number of iterations needed to get the result. - The program should run continually until the user enters -99 to stop. Sample Output: enter x 0.8 Re-enter x, it should be >=-0.5 and <=0.5 -0.8 Re-enter x, it should be >=-0.5 and <=0.5 0.5 the actual value is 26.565073 deg. the series value is 26.618687 deg. number of iterations = 3 enter x -99 End, Thank you

Solve using C language

Answer 1

 #include <stdio.h> #include <math.h> #include <stdlib.h> #define PI 3.14159265359 int main(){ double x; while(1){ printf("enter x\n"); scanf("%lf", &x); if(x==-99){ printf("End, Thank you\n"); return 0; } if(fabs(x)>0.5){ printf("Re-enter x, it should be >=-0.5 and <=0.5\n"); } else{ double aTan_actual = atan(x); double aTan_calculated = 0.0; // dhyan dena hai yha int count = 0; int i=1; while(fabs(aTan_actual - aTan_calculated)*(180.0/PI) > 0.001){ if(i%4 == 1) aTan_calculated += pow(x, (double)i)/(double)i; if(i%4 == 3) aTan_calculated -= pow(x, (double)i)/(double)i; i+=2; count++; } printf("the actual value is %lf deg.\n", aTan_actual*(180.0/PI)); printf("the series value is %lf deg.\n", aTan_calculated*(180.0/PI)); printf("number of iterations = %d\n\n",count); } } }

// Note that number of iteration may differ due to different value of PI used and different datatype used.

// compile the code with      gcc filename.c -lm      (for math.h header)