C++ Program to calculate the value of sin(x) and cos(x)

Given with the input as angles and the task is to calculate the value of sin(x) and cos(x) corresponding to the given angle and display the result

For Sin(x)

Sin(x) is a trigonometric function which is used to calculate the value of x angle.

Formula

$$\sin (x) = \displaystyle\sum\limits_{k=0}^\infty \frac{(-1)^{k}}{(2k+1)!}x^{2k+1}$$

For Cos(x)

Cos(x) is a trigonometric function which is used to calculate the value of x angle.

Formula

$$\cos (x) = \displaystyle\sum\limits_{k=0}^\infty \frac{(-1)^{k}}{(2k)!}x^{2k}$$

Approach used in the below program is as follows −

• Input the value of x angle for sin(x) and cos(x)
• Apply the formulas given for sin(x) and cos(x)
• Print the result

ALGORITHM

START Step 1-> declare function to calculate value of sin    void cal_sin(float n)    declare and set float acc = 0.0001, denominator, sinx, sinval    Set n = n * (3.142 / 180.0)    Declare float temp = n    Set sinx = n    Set sinval = sin(n)    Declare and set int i = 1    DO       set denominator = 2 * i * (2 * i + 1)       set temp = -temp * n * n / denominator       Set sinx = sinx + temp       Set i = i + 1    While(acc <= fabs(sinval - sinx))       print sinx Step 2-> Declare function to calculate value of cos    void cal_cos(float n)    Declare and set float acc = 0.0001, temp, denominator, cosx, cosval    Set n = n * (3.142 / 180.0)    Set temp = 1    set cosx = temp    set cosval = cos(n)    Set int i = 1    Do       set denominator = 2 * i * (2 * i - 1)       Set temp = -temp * n * n / denominator       Set cosx = cosx + temp       Set i = i + 1    While(acc <= fabs(cosval - cosx))       print cosx Step 3-> In main()    Declare float n = 30    Call cal_sin(n0    set n=60    Call cal_cos(n) STOP

Example

#include <iostream> #include <math.h> using namespace std; //calculate value of sin void cal_sin(float n) {         float acc = 0.0001, denominator, sinx, sinval;     n = n * (3.142 / 180.0);  //convert in radian     float temp = n;     sinx = n;               sinval = sin(n);         int i = 1;     do {         denominator = 2 * i * (2 * i + 1);         temp = -temp * n * n / denominator;         sinx = sinx + temp;         i = i + 1;     } while (acc <= fabs(sinval - sinx));     cout<<sinx; } //calculate value of cos   void cal_cos(float n) {     float acc = 0.0001, temp, denominator, cosx, cosval;     n = n * (3.142 / 180.0); //convert in radiam     temp = 1;     cosx = temp;               cosval = cos(n);     int i = 1;     do {         denominator = 2 * i * (2 * i - 1);         temp = -temp * n * n / denominator;         cosx = cosx + temp;         i = i + 1;     } while (acc <= fabs(cosval - cosx));     cout<< cosx; } int main() {     float n = 30;     cout<<"value of Sin is : "; cal_sin(n); cout<<"\n";     n=60; cout<<"value of Cos is : "; cal_cos(n);     return 0; }

Output

value of Sin is : 0.500061 value of Cos is : 0.499847