Question

Problem 1: The series expansion for cos, and sin, functions and trigonometric identities are as follows (r in radians) 6 20 Points cos x = 1-2, + sin(2x) = 2 sinx cosx cos(2x) cos2 -sin2

a.) Write a C++ program that calculates the value of the series sin x and cos x, sin 2x or cos 2x where the user enters the value of x (in degrees) and n the number of terms in the series. For example, if n= 5, the program should calculate the sum of 5 terms in the series for a given values of x. The program should use switch statements to determine the choice sin x AND cos x, sin 2x OR cos 2x. (Note: you may have to convert degrees to radians for sin and cos functions.)

b.) Draw a detailed flow chart on how this program is designed, indicating the necessary inputs, outputs and thealgorithm you have used.

Answer 1

#include<iostream>
using namespace std;

long long int factorial(int n)
{
int f=1,i;
for(i=2;i<=n;i++)
f*=i;
return f;
}

double sine(int n, double x)
{
int i;
double ans = x,tmp=1,exp=x;

for(i=1;i<n;i++)
{
tmp+=2;
exp*=x*x;
if(i%2)
ans-=exp/factorial(tmp);
else
ans+=exp/factorial(tmp);
}
return ans;
}

double cosine(int n, double x)
{
int i;
double ans = 1,tmp=0,exp=1;

for(i=1;i<n;i++)
{
tmp+=2;
exp*=x*x;
if(i%2)
ans-=exp/factorial(tmp);
else
ans+=exp/factorial(tmp);
}
return ans;
}

int main()
{
int n,choice;
double x,ans,tmp;

cout<<"Enter the angle and number of terms to be added\n";
cin>>x>>n;

x= x * 22 / (7 * 180); //Degree to radian

cout<<"1.sinx & cosx\n2.sin2x\n3.cos2x\n";
cin>>choice;

switch(choice)
{
case 1:
cout<<"sinx = "<<sine(n,x)<<endl;
cout<<"cosx = "<<cosine(n,x)<<endl;
break;

case 2:
cout<<"sin2x = "<<2*sine(n,x)*cosine(n,x)<<endl;
break;

case 3:
cout<<"cos2x = "<<cosine(n,x)*cosine(n,x)-sine(n,x)*sine(n,x)<<endl;
break;
}
}

START INPUT x,n & choicc Convert x to radians CHoose function sin2x cos2x sinx & cosx OUTPUT THE ANSWER STOP