# Class Math. Overview. Trigonometric functions. Examples

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##### 1. General information about the Math class

The java.lang library contains tools for performing mathematical calculations, in particular, the well-known Math class. This class implements math functions that operate on floating point numbers. Class functions are divided into the following groups:

• trigonometric functions;
• exponential functions;
• rounding functions;
• other special functions.

The class also contains two constants, the access to which is as follows:

• Math.PI – Pi number (3.14…);
• Math.E – exponent (2.71…).

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##### 2. Trigonometric functions. The list

Trigonometric functions of the Math class allow you to get the numerical value of a known mathematical function. These functions operate in radians. If degrees are known, then to get radians, you need to use a conversion formula like

`radians = Math.PI * degree / 180;`

here

• degree – angle specified in degrees;
• Math.PI – number 3.1415. This is a constant from the Math class.

The list of trigonometric functions in the Math class is as follows

• sin(x) – returns the sine of angle x, given in radians;
• cos(x) – calculates the cosine of the angle x;
• tan(x) – calculates the tangent of the angle x.

Accordingly, the declaration of functions in the Math class has the form

```static double sin(double x)
static double cos(double x)
static double tan(double x)```

where x is the angle value given in radians.

Example.

```public class MathFunctions {

public static void main(String[] args) {
// 1. Angle set to 45 degrees
double degree = 45; // given angle in degrees

// 2. Get radians from degrees
double radian = Math.PI * degree / 180;

// 3. Get the sine of a 45 degree angle

// 4. Get the cosine

// 5. Get the tangent

// 6. Print the result
System.out.println("resSin = " + resSin);
System.out.println("resCos = " + resCos);
System.out.println("resTan = " + resTan);
}
}```

Program result

```resSin = 0.7071067811865475
resCos = 0.7071067811865476
resTan = 0.9999999999999999```

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##### 3. Inverse trigonometric functions. The list. Example

Inverse trigonometric functions take the result of the corresponding trigonometric function and return the angle in radians. If necessary, the resulting value in radians can be converted to degrees using the formula:

`degree = 180 * radians / Math.PI;`

here

• degree – angle in degrees;
• Math.PI – number 3.1415. This is a constant from the Math class.

The list of inverse trigonometric functions is as follows:

• asin() – arcsine of the number;
• acos() – arc cosine;
• atan() – arc tangent of a numeric value;
• atan2() – arc tangent given by x/y proportion.

The declaration of inverse trigonometric functions is as follows

```static double asin(double value)
static double acos(double value)
static double atan(double value)
static double atan2(double x, double y)```

here

• value – some numeric value. For the asin() and acos() functions, value must be between [0; 1].

Example.

```public class MathFunctions {

public static void main(String[] args) {
// 1. Set a value
double value = 1.0;

// 2. Get arccosine, result in radians
double aCos = Math.acos(value); // aCos = 0 radians
System.out.println("arcCos(1.0) = " + aCos);

// 3. Get the arcsine
double aSin = Math.asin(value); // aSin = 1.57079 radians
System.out.println("arcSin(1.0) = " + aSin);

// 4. Get arctangent.
//   Form a value that corresponds to an angle of 45 degrees
value = 1;
double aTan = Math.atan(value); // aTan = 0.78 radians
System.out.println("aTan = " + aTan);

// 5. Get the arctangent from the aspect ratio
double aTan2 = Math.atan2(1, 1); // angle 45 degrees
System.out.println("aTan2 = " + aTan2); // aTan2 = 0.78
}
}```

Program result

```arcCos(1.0) = 0.0
arcSin(1.0) = 1.5707963267948966
aTan = 0.7853981633974483
aTan2 = 0.7853981633974483```

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##### 4. Hyperbolic functions

Hyperbolic functions return a value from an argument specified in radians

• sinh() – hyperbolic sine;
• cosh() – hyperbolic cosine;
• tanh() – hyperbolic tangent.

The declaration of hyperbolic functions is as follows

```static double sinh(double x)
static double cosh(double x)
static double tanh(double x)```

here

• x – value in radians.

Example.

```public class MathFunctions {

public static void main(String[] args) {
// 1. Set a value
double value = 1.0;

// 2. Sine hyperbolic
double SinH = Math.sinh(value);
System.out.println("SinH = " + SinH);

// 3. Cosine hyperbolic
value = 1.0;
double CosH = Math.cosh(value);
System.out.println("CosH = " + CosH);

// 4. Tangent hyperbolic
value = 1.0;
double TanH = Math.tanh(value);
System.out.println("TanH = " + TanH);
}
}```

Program result

```SinH = 1.1752011936438014
CosH = 1.543080634815244
TanH = 0.7615941559557649```