Introduction

To manage the measurements and other related operations, the circumference is divided into 360 portions. Each of these portions is called a degree. The unit used to represent the degree is the degree, written as ˚. Therefore, a circle contains 360 degrees, that is 360˚. The measurement of two points A and D of the circumference could have 15 portions of the circumference. In this case, this measurement would be represents as 15˚.

The distance between two equidistant points A and B is a round shape geometrically defined as an arc. An angle, ө, is the ratio of the distance between two points A and B of the circumference divided by the radius R. This can be written as:

Therefore, an angle is the ratio of an arc over the radius. Because an angle is a ratio and not a “physical” measurement, which means an angle is not a dimension, it is independent of the size of a circle. Obviously this angle represents the number of portions included by the three points. A better unit used to measure an angle is the radian or rad.

A cycle is a measurement of the rotation around the circle. Since the rotation is not necessarily complete, depending on the scenario, a measure is made based on the angle that was covered during the rotation. A cycle could cover part of the circle in which case the rotation would not have been completed. A cycle could also cover the whole 360˚ of the circle and continue there after. A cycle is equivalent to the radian divided by 2 * Pi.

The word п, also written as Pi, is a constant number used in various mathematical calculations. Its approximate value is 3.1415926535897932. The calculator of Windows represents it as 3.1415926535897932384626433832795. Borland had included its value in the math.h library as M_PI 3.14159265358979323846.

A diameter is two times the radius. In geometry, it is written as 2R. In C++, it is written as 2 * R or R * 2 (because the multiplication is symmetric). The circumference of a circle is calculated by multiplying the diameter to Pi, which is 2Rп, or 2 * R * п or 2 * R * Pi.

A radian is 2Rп/R radians or 2Rп/R rad, which is the same as 2п rad or 2 * Pi rad.

To perform conversions between the degree and the radian, you can use the formula:

360˚ = 2п rad which is equivalent to 1 rad = 360˚ / 2п = 57.3˚.

Consider the following geometric figure:

Consider AB the length of A to B, also referred to as the hypotenuse. Also consider AC the length of A to C which is the side adjacent to point A. The cosine of the angle at point A is the ratio AC/AB. That is, the ratio of the adjacent length, AC, over the length of the hypotenuse, AB:

The returned value, the ratio, is a double-precision number between –1 and 1.

To calculate the cosine of an angle, the Math class provides the Cos() method. Its syntax is:

public static double Cos(double d);

Here is an example:

using System;

class Program
{
    static int Main()
    {
        int number = 82;
        
        Console.WriteLine("The cosine of {0} is {1}", number, Math.Cos(number));
	
        return 0;
    }
}

This would produce:

The cosine of 82 is 0.949677697882543
Press any key to continue . . .

Consider AB the length of A to B, also called the hypotenuse to point A. Also consider CB the length of C to B, which is the opposite side to point A. The sine represents the ratio of CB/AB; that is, the ratio of the opposite side, CB over the hypotenuse AB.

To calculate the sine of a value, you can call the Sin() method of the Math class. Its syntax is:

public static double Sin(double a);

Here is an example:

using System;

class Program
{
    static int Main()
    {
        double number = 82.55;
        
        Console.WriteLine("The sine of {0} is {1}", number, Math.Sin(number));
	
        return 0;
    }
}

This would produce:

The sine of 82.55 is 0.763419622322519
Press any key to continue . . .

Consider AC the length of A to C. Also consider BC the length of B to C. The tangent is the result of BC/AC; that is, the ratio of BC over AC. To assist you with calculating the tangent of of a number, the Math class is equipped with a method named Tan whose syntax is:

public static double Tan(double a);

Here is an example:

using System;

class Program
{
    static int Main()
    {
        uint number = 225;
        
        Console.WriteLine("The tangent of {0} is {1}", number, Math.Tan(number));
	
        return 0;
    }
}

This would produce:

The tangent of 225 is -2.53211499233434
Press any key to continue . . .

Consider BC the length of B to C. Also consider AC the length of A to C. The arc tangent is the ratio of BC/AC. To calculate the arc tangent of a value, you can use the Math.Atan() method. Its syntax is

public static double Atan(double d);

Here is an example:

using System;

class Program
{
    static int Main()
    {
        short number = 225;
        
        Console.WriteLine("The arc tangent of {0} is {1}",
			  number, Math.Atan(number));
	
        return 0;
    }
}

This would produce:

The arc tangent of 225 is 1.56635191161394
Press any key to continue . . .