# Hyperbolic Functions in C Standard Library

Question: What are Different Hyperbolic Functions in Standard C Library?

Answer: We have following hyperbolic functions defined and prototyped in ‘math.h’ header.

```   double sinh(double angle);
double cosh(double angle);
double tanh(double angle);```

These functions return the hyperbolic sine, hyperbolic cosine and hyperbolic tangent of their arguments respectively. Each function takes angle, in radians, as its argument. Let’s learn to use ‘sinh()’ in a C program below,

```/* fp_sinhyperbolic_fun.c -- 'sinh()' returns hyperbolic sine of */
#include <stdio.h>
#include <stdlib.h>
#include <math.h>

int main(void)
{
double angle, result;

printf("User, write in angle ,in radians, whose hyperbolic sine "
"to be computed...\n");
scanf("%lf", &angle);

/* calling 'sinh()' to compute hyperbolic sine of angle */
result = sinh(angle);

printf("hyperbolic sine of \"angle: %lf\" is:%lf\n",
angle, result);

return 0;
}```

The sinh() function returns the hyperbolic sine of angle, say x, which is defined mathematically as:

`           sinh(x) = (exp(x) - exp(-x)) / 2`

Output of the above program follows:

```User, write in angle ,in radians, whose hyperbolic sine to be computed...
+0.0
hyperbolic sine of "angle: 0.000000" is:0.000000

User, write in angle ,in radians, whose hyperbolic sine to be computed...
-0.0
hyperbolic sine of "angle: -0.000000" is:-0.000000

User, write in angle ,in radians, whose hyperbolic sine to be computed...
10
hyperbolic sine of "angle: 10.000000" is:11013.232875

User, write in angle ,in radians, whose hyperbolic sine to be computed...
1000000000000000
hyperbolic sine of "angle: 1000000000000000.000000" is:inf```

Observe the last case where output turned out as ‘inf’, short for infinity, for very large angle. Try using other functions to see their outputs.

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