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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
Updated on: 20-Nov-2019
4K+ Views
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