C# Program to Find the Value of Sin(x)
Sin(x) is also known as Sine. It is a trigonometric function of an angle. In a right-angled triangle, the ratio of the length of the perpendicular to the length of the hypotenuse is known as the sine of an angle.
sin θ = perpendicular / hypotenuse
The values of sine of some of the comman angles are given below,
- sin 0° = 0
- sin 30° = 1 / 2
- sin 45° = 1 / √2
- sin 60° = √3 / 2
- sin 90° = 1
This article focuses upon how we can calculate the sine of an angle by in C#.
We can calculate the sine of an angle by using the inbuilt sin() method. This method is defined under the Math class and is a part of the system namespace. Math class is quite useful as it provides constants and some of the static methods for trigonometric, logarithmic, etc.
public static double Sin (double angle);
- angle: A double value (angle in radian)
- double: If “angle” is double
- NaN: If “angle” is equal to NaN, NegativeInfinity, or PositiveInfinity
The value of sin(0) = 0 The value of sin(45) = 0.707106781186547 The value of sin(90) = 1 The value of sin(135) = 0.707106781186548
Sine of angle1: NaN Sine of angle2: NaN Sine of angle3: NaN
We can calculate the value of sine of an angle using Maclaurin expansion. So the Maclaurin series expansion for sin(x) is:
sin(x) = x - x3 / 3! + x5 / 5! - x7 / 7! + ....
Follow the steps given below to find the value of sin(x):
- Initialize a variable angleInDegree that stores the angle (in degree) to be calculated.
- Initialize another variable terms that stores the number of terms for which we can approximate the value of sin(x).
- Declare a global function findSinx.
- Declare a variable current. It stores the angle in radians.
- Initialize a variable answer with current. It will store our final answer.
- Initialize another variable temp with current.
- Iterate from i = 1 to i = terms. At each step update temp as temp as ((-temp) * current * current) / ((2 * i) * (2 * i + 1)) and answer as answer + temp.
- Eventually, return the answer from findSinX function.
- Print the answer.
This formula can compute the value of sine for all real values of x.
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