Mathematical C

C doesn't define advanced mathematical functions like cosine, logarithms or Bessel functions in the language itself. However, programmers have written functions that perform these operations and others. These functions are gathered together in the math library.

When using the math library, we need to include the math header file as illustrated in Part 1-1.

#include <math.h>

This header file give us the prototypes for the functions in the math library. (We'll see how this is done in Part 2-7.) These prototypes tell us that most of the functions in the math library take arguments of type double and also return double precision floating point numbers. Among the prototypes in the file math.h are the following math functions:

	`double sin( double x ) ;` - sine of x
	`double cos( double x ) ;` - cosine of x
	`double tan( double x ) ;` - tangent of x
	`double asin( double x ) ;` - arc sine of x
	`double acos( double x ) ;` - arc cosine of x
	`double atan( double x ) ;` - arc tangent of x
	`double exp( double x ) ;` - e to the x power
	`double log( double x ) ;` - natural logarithm of x
	`double log10( double x ) ;` - common logarithm of x
	`double pow( double x, double y ) ;` - x to the y power
	`double sqrt( double x ) ;` - square root of x

One thing to remember is that all of the trigonometric functions (sin, cos, tan, asin, acos and atan) deal in radians instead of degrees. So, for example, sin( 1.57 ) will return a number about 1.0.

Even though the math functions are defined to use double precision numbers, C's type handling will do what you expect if you use single precision floating point numbers as arguments or assign the return values to single precision numbers. For example,

float x, y ;

y = sqrt( x ) ;

will work perfectly well. However, for reasons of performance and computational accuracy it is usually advisable to go ahead and declare such variables as double precision.

As long as we're looking at using double precision numbers so extensively, we should learn how to read them in and write them out. The easy part is printing doubles. We do the same thing using printf() as we do for single precision floats. Specifically,

double x ;

...
printf( "%f", x ) ;

is the proper way to print out double precision floating point numbers. However, the same is not true of scanf(). Here, we have a different format specifier for the double precision numbers. To read in such a number, we'd use code like:

double x ;

...
scanf( "%lf", &x ) ;

Notice that the format specifier for reading doubles is %lf. This specifier can also be used when printing doubles, but it is not necessary.

By way of review, let us note that if we have a right triangle, the cosine of the angle between the hypotenuse and a side is equal to the ratio of the length of the adjacent side to the length of the hypotenuse. So if we have this ratio, then we can find the angle by using the arc cosine (acos()) function. We can also find the other angle by applying this procedure to the ratio of the other side to the hypotenuse.

Write a C expression (not the whole statement) to compute the angle given the lengths of the two sides stored in the variables, adjacent and hypotenuse.