C# program to find the value of Sin(x)

Introduction

In this article, we will learn about C# program to find the value of Sin(x). Sine is another name for Sin(x). This is a trigonometric angle formula. The sine of an angle is the ratio of the length of the hypotenuse to the length of the perpendicular in a right trapezoid. The powerful computer language C# can be used to solve challenging mathematical problems. Finding the value of sin(x), where x is any angle in radians, is one of these problems. In this article, we will learn how to use the Math library to create a C# program that calculates the value of sin(x). The mathematical foundations of the sin function will also be covered, as well as some of its real-world applications. Whether you are a newbie or an experienced programmer, this article will provide you with helpful tips on how to do calculations with C#. So let’s start learning how to calculate sin(x) in C

#method

By using the built-in sin() function, we can determine the sine of an angle. This method is specified under the Math class and is part of the system namespace. Teaching mathematics is very helpful because it covers constants and some static trigonometry, logarithms, and other methods.

In addition to this method used directly in our code, there is another very important method considering the output console, that is -

By using the MacLaughlin expansion, we can determine the sine of the angle. Therefore, the Maclaurin series of sin(x) expands to

algorithm

To calculate the value of sin(x), follow the instructions below -

Step 1 − Set the angle to be calculated (in degrees) into the variable angleInDegree.

Step 2 − Create a new variable called terms to store how many terms we can use to estimate the value of sin.(x).

Step 3 −Declare the findSinx global function.

Step 4 − Establish a fluctuation flow. Directions are saved in radians.

Step 5 − Use current to initialize the variable response. It will save our complete response.

Step 6 − Use current to initialize the temperature of another variable.

Step 7 − Repeat from item 1 to item i. Update the temperature of each stage to ((-temp) * current * current) / ((2 * i) * (2 * i 1)) and update the answer to ((answer temp)).

Step 8 − Finally, the results of the findSinX method are given.

Step 9 − Print the solution.

Example

// C# program to illustrate how we can
// calculate the value of sin(x)
// using Maclaurin's method

using System;
class SINE{
   static double findSinX(int angleInDegree, int terms) {

      // Converting angle in degree into radian
      double current = Math.PI * angleInDegree / 180f;

      // Declaring variable to calculate final answer
      double answer = current;
      double temp = current;

      // Loop till number of steps provided by the user
      for(int i = 1; i <= terms; i++) {

         // Updating temp and answer accordingly
         temp = ((-temp) * current * current) / ((2 * i) * (2 * i + 1)); 
         answer = answer + temp;
      }
      
      // Return the final answer
      return answer;
   }
   
   // Driver code
   static public void Main() {

      // Angle in degree
      int angleInDegree1 = 45;
      
      // Number of steps
      int terms1 = 10;
      
      // Calling function to calculate sine of angle
      double answer1 = findSinX(angleInDegree1, terms1);
      
      // Print the final answer
      Console.WriteLine("The value of sin({0}) = {1}", angleInDegree1, answer1);

      // Angle in degree
      int angleInDegree2 = 90;

      // Number of steps
      int terms2 = 20;
      
      // here we are calling function to calculate sine of angle
      double result2 = findSinX(angleInDegree2, terms2);
      
      // Print the final answer
      Console.WriteLine("The value of sin({0}) = {1}",
      angleInDegree2, result2);

      // Angle in degree
      int angleInDegree3 = 135;
      
      // Number of steps
      int terms3 = 30; 
      
      // Calling function to calculate sine of angle
      double result3 = findSinX(angleInDegree3, terms3);
      
      // Print the final answer
      Console.WriteLine("The value of sin({0}) = {1}",  angleInDegree3, result3);

      // Angle in degree
      int angleInDegree4 = 180;
      
      // Number of steps
      int terms4 = 40;

      // Calling function to calculate sine of angle
      double result4 = findSinX(angleInDegree4, terms4);
      
      // Print the final answer
      Console.WriteLine("The value of sin({0}) = {1}",  angleInDegree4, result4);
   }
}

Output

The value of sin(45) = 0.707106781186547
The value of sin(90) = 1
The value of sin(135) = 0.707106781186548
The value of sin(180) = 2.34898825287367E-16

time complexity

In this particular program to find the value of Sin(x), we get the time complexity: O(n). //n is the number of terms passed as input.

The space complexity is O(1).

in conclusion

In summary, creating a C# program to calculate sin(x) is a fairly simple process that can be performed using the Math library. Programmers can use this knowledge to build more complex mathematical algorithms and applications by understanding the mathematical ideas behind the sin function.

Engineering, physics, and computer graphics are just some real-world uses for knowing how to calculate sin values. For example, the sine function is often used to simulate fluctuations, provide visual effects, and manage robotic systems.

In summary, learning how to use the sin function and the C# programming language can provide programmers with a valuable set of abilities that can be used to solve a variety of complex mathematical problems in a variety of fields.

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