Scan the angle in degrees x_deg. Express this angle in radians, and then calcula
ID: 3631522 • Letter: S
Question
Scan the angle in degrees x_deg. Express this angle in
radians, and then calculate Y=sin(x)+cos(x) by
using the math.h library of functions. Compare the so
calculated value of Y with the approximate value y
obtained by using n_term terms of the Taylor series for
each of
sin(x)=Sum[(-1)^n x^(2n+1)/(2n+1)!] (n goes from 0 to n_term-1)
and
cos(x)=Sum[(-1)^n x^(2n)/(2n)!] (n goes from 0 to n_term-1).
Scan an integer value of n_term. Evaluate (2n)! and (2n+1)! by embedded
for-loop statements. Use two do/while statements to continue
the calculations for different n_term and different x_deg. For
example, use flag=1 to continue calculations for different n_term
within the inner do/while loop, and flag=0 to exit that loop.
Use Flag=1 to continue calculations for different x_deg
within the outer do/while loop, and Flag=0 to exit that loop.
Use %g format for all double values. Use double declaration
when calculating k! (because k! for large k becomes quickly
too big for integer declaration).
.................................................................
Your output should look like this:
Calculation of true and approximate values of sin(x)+cos(x)
Enter x_deg: 30
True value of sin(30)+cos(30) = 1.36603
n_term approximation of sin(30)+cos(30)
Enter number of terms:
2
Explanation / Answer
#include <iostream.h>
#include <cmath.h>
using namespace std;
double fac(int n)
{
double f=n;
while (--n)f*=n;
return f;
}
int main()
{
double long x;
cout << "Enter Angle in Radians: " << endl;
cin >> x;
double cos(0.0);
double temp(0.0);
for (int i=0; i<170; i++){
if (i%2 == 1)
temp = (pow(x,i*2+2))/(fac(i*2+2));
else
temp = (-1)*(pow(x,i*2+2))/(fac(i*2+2));
if (temp <= 0.0001)
break;
else
cos += temp;
}
cout << "Cosine of Angle is: " << cos << endl;
system("PAUSE");
return 0;
}