You already know that C++ provides different built in data types to work with numbers. The ranges of the data types are discussed in the “C++ Data Types” article. Now we will discuss a little bit more advanced techniques to work with numbers.

C++ library called cmath offers capability to perform different mathematical operations with numbers. To be able to use these functions you have to add an include statement in your program:

```
//use math
#include <cmath>
```

Now you can use the following capabilities of cmath:

### 1. Trigonometric functions

sine, cosine, tangent. All these functions take a double value of the radians as the parameter:

```
const double PI = 3.141592653589793238463;
//convert 60 angles to radians
double angle = 60 * PI / 180;
cout << "sine of 60 is " << sin(angle) << endl;
cout << "cosine of 60 is " << cos(angle) << endl;
cout << "tangent of 60 is " << tan(angle) << endl;
```

It produces the following output:

sine of 60 is 0.866025

cosine of 60 is 0.5

tangent of 60 is 1.73205

### 2. length of the hypotenuse

You can get the length of the hypotenuse for a right angled triangle with the sides of length “a” and “b” – hypot(a, b):

```
cout << "The hypotenuse of the right triangle with one side 3 and the other 4 is " << hypot(3.0, 4.0) << endl;
```

### 3. Natural logarithm functions

It takes as the parameter double value and returns it’s natural logarithm:

```
cout << "The natural logarithm of 10 is " << log(10) << endl;
```

### 4. Absolute value

There are two different functions to get the absolute value of an integer

```
int abs(int) and of a double value double fabs(double):
cout << "The absolute value of -10 is " << abs(-10) << endl;
cout << "The absolute value of 12.71 is " << fabs(12.71) << endl;
```

### 5. Square Root

To get the square root of a double value use sqrt(double) function:

```
cout << "The square root of 16 is " << sqrt(16.0) << endl;
```

### 6. Power

If you want to rise a double number to a power, you can use power(double base, double power):

```
cout << "2 to the power 3 is " << pow(2.0,3.0) << endl;
```

If you will put all these lines of examples in one program, you will get the following output:

sine of 60 is 0.866025

cosine of 60 is 0.5

tangent of 60 is 1.73205

The hypotenuse of the right triangle with one side 3 and the other 4 is 5

The natural algorithm of 10 is 2.30259

The absolute value of -10 is 10

The absolute value of 12.71 is 12.71

The square root of 16 is 4

2 to the power 3 is 8

## Random Number in C++

Sometimes you will need to use random numbers in your programs. For this purpose you can use two functions from library cstdlib and time data type from ctime. You need to add the following include statements in your program:

```
#include <cstdlib>
#include <ctime>
```

If you want that your program should always generates a new sequence of random numbers – you need to set a seed to random generator according to the current time. It can be done in the following way:

```
//set random seed
srand(time_t(NULL));
After this you can get a random number by using rand() function:
//generate a random numbers sequence
for (int i = 0; i != 5; ++i)
cout << "This is a random number " << rand() << endl;
```

Here is 5 random numbers, generated by this code:

This is a random number 38

This is a random number 7719

This is a random number 21238

This is a random number 2437

This is a random number 8855

## Get Random Number in Specific Range

But often your task will be to get a sequence of random numbers in a specified range. To get only numbers in the range from min to max you can use this code:

```
int min = 5;
int max = 12;
cout << "This is a random number in range from 5 to 12 " << min + (rand() % (int)(max - min + 1)) << endl;
```

The below expression

```
min + (rand() % (int)(max - min + 1))
```

returns a random value in range from min to max

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