Predefined functions in math.h

abs  - abs(1.45) is ___ , abs(-1.45) is ____

sqrt(25) is ____  result is type ____

pow(x, y) is xy

pow(3, 2) is ___   pow(2, 3) is _____, result is type ___

floor  , ceil convert a real value to a whole number (also 
type real).

x is 4.15
   floor(x)        x         ceil(x)
         4.0      4.15           5.0   …    6.0    7.0

x is -8.65
    
    floor(x)     x      ceil(x)
       -9.0      -8.65     -8.0    …   -7.0       -6.0     

sin, cos, tan  - trigonometric functions.  Argument should 
be in radians, not degrees.

   If x is an angle in radians, cos(x) returns the cosine of x.

   converting from degrees to radians - 
0 degrees is 0 radians
	360 degrees is 2 ? radians
 
  in general, if w is in degrees, to convert to radians, 
mulitply by ? / 180.0

if theta_deg is angles in degrees,

   theta_rad = theta_deg * 3.14159 / 180.0;


/* program to convert angle in degrees to radians 
 * and print its sin and cosine
 */

#include <stdio.h>
#inlcude <math.h>

#define PI 3.14159

int main(void)
{
   double rad_per_degree = PI / 180.0;

   double theta_deg, theta_rad;

   printf("Enter theta in degrees: ");
   scanf("%lf", &theta_deg);

  theta_rad = theta_deg * rad_per_degree;
  printf("Theta in radians is %.2f\n", theta_rad);
  printf("Its sin is %f and its cosine is %f\n", 
             sin(theta_rad), cos(theta_rad));
  return (0);
}

[thunder] ~ > cc -lm degrees.c
[thunder] ~ > a.out
Enter theta in degrees:90
Theta in radians is 1.57
Its sin is 1.000000 and its cosine is 0.000001
[thunder] ~ > a.out
Enter theta in degrees:180
Theta in radians is 3.14
Its sin is 0.000003 and its cosine is -1.000000

Writing your own functions

Example in book:  Drawing some stick figures using 
standard shapes, triangle, square, circle. 

We can write our own functions to draw such shapes and 
then call them just like we call library functions.

/* “Draws” a square */
void draw_square() 
{
   printf(“*******\n”);
   printf(“*     *\n”);
   printf(“*     *\n”);
   printf(“*     *\n”);
   printf(“*******\n”);
}


Assume you have draw_circle, 
draw_triangle, draw_square functions:

#include <stdio.h>

/* function prototypes */
void draw_square();
void draw_circle();
void draw_triangle();

void main()
{
   draw_circle();   /* circle on top */
   draw_triangle(); /* triangle next */
   draw_square();  /* square on bottom*/

   return 0;
}

/* function definitions go here. Order
 * doesn’t matter
 */
/* “Draws” a square */
void draw_square() 
{
   printf(“*******\n”);
   printf(“*     *\n”);
   printf(“*     *\n”);
   printf(“*     *\n”);
   printf(“*******\n”);
}

Flow of execution for above program:

Begin to execute main function:
   Execute 1st line of main - call to draw_circle
         Execute first line of draw_circle
         …
         Execute last line of draw_circle and return
         to where you left off In function main.

   Execute 2nd line of main function – 
               call to draw_triangle
         Execute first line of draw_triangle
         …
         Execute last line of draw_triangle and return

   Execute 3rd line of main function – 
              call to draw_square
         Execute first line of draw_square
         …
         Execute last line of draw_square and return
   Execute last line of main function and return 0.

Function definition has the form:

Result type   function name   argument list
void      draw_square    () 
{
      function body
}

A void function does not return a result – it performs 
an action such as printing or displaying but doesn’t 
calculate a value (unlike sin or sqrt).


Other uses of void functions:

Displaying instructions to the program user to help 
the user understand how to interact with the program.

void instruct()
{
  printf(“This program multiplies ”);
  printf(“two fractions.\n”);
  printf(“Enter each one as: ”);
  printf(“n / d \n”);
  printf(“where n and d are ”);
  printf(“both integers.\n”);
}

When called this function displays:

This program multiplies two fractions.
Enter each one as: n / d
where n and d are both integers.


#include <stdio.h>

void instruct();

int main()
{
   integer num_1, denom_1;
   …

   /* Display instructions */
   instruct();

   /* Read two fractions */
   printf(“Enter first fraction: “);
   scanf(“%d/%d”, &num_1, &denom_1);
   …

   return 0;
}  /* end of main */


void instruct()
{
  printf(“This program multiplies ”);
  printf(“two fractions.\n”);
  …
}   /* end of instruct */