What am I doing wrong with my code for Mclaurin Series Expansion?

(https://i.stack.imgur.com/3LgGA.png) I have been trying to make a code in c++ for the Mclaurin ’s Series expansion of sin(x), as a review for my Intro to Programming class and my results are always not equivalent to the sample runs. I have been trying to trouble shoot this for hours to no avail. Please help.

#include <iostream>
#include <cmath>
#include <iomanip>
using namespace std;
double factorial(int num);
double sum(double number, int n);
int main() {
double number, sin;
int n;
    cout<<"Enter the value of x: ";
    cin>>number;
    cout<<"Enter the number of terms: ";
    cin>>n;
    sin=sum(number,n);
    cout<<"sin("<<number<<") = "<<fixed<<showpoint<<setprecision(6)<<sin<<endl;

    return 0;
}
double factorial(int num){
    double sum=1;
    for(int x=num; x>=1;x--){
        sum*=x;
    }
    return sum;
}
double sum(double number, int n){
    int count=3;
    double term,term1, sum=0, sum2=0, totalSum;

    for(int i=1;i<n-1;i+=2 ){
        term1=(pow(number, count))/ factorial(count);
        sum+=term1;
        count+=4;
        }
    for(int j=0;j<n-2;j+=2){
            term=pow(number, count)/ factorial(count);
            sum2+=term;
            count+=4;
        }
    totalSum=number+sum+sum2;
    return totalSum;
    }