Mathematics

122 15. Mathematics It's your favorite subject: Mathematics! Hello, I'm Doctor Math, and I'll be making math FUN and EASY! [vomiting sounds] Ok, I know math isn't the grandest thing for some of you out there, but these are merely functions that quickly and easily do math you either know, want, or just don't care about. That pretty much covers it. For you trig fans out there, we've got all manner of things, including sine, cosine, tangent, and, conversely, arc sine, arc cosine, and arc tangent. That's very exciting. And for normal people, there is a slurry of your run-of-the-mill functions that will serve your general purpose mathematical needs, including absolute value, hypotenuse length, square root, cube root, and power. In short, you're a fricking MATHEMATICAL GOD! Oh wait, before then, I should tell you that the trig functions have three variants with different suffixes. The “f” suffix (e.g. sinf()) returns a float, while the “l” suffix (e.g. sinl()) returns a massive and nicely accurate long double. Normal sin() just returns a double. These are extensions to ANSI C, but they should be supported by modern compilers. Also, there are several values that are defined in the math.h header file. M_E e M_LOG2E log_2 e M_LOG10E log_10 e M_LN2 log_e 2 M_LN10 log_e 10 M_PI pi M_PI_2 pi/2 M_PI_4 pi/4 M_1_PI 1/pi M_2_PI 2/pi Beej's Guide to C Programming 123 M_2_SQRTPI 2/sqrt(pi) M_SQRT2 sqrt(2) M_SQRT1_2 1/sqrt(2) Beej's Guide to C Programming 124 15.1. sin(), sinf(), sinl() Calculate the sine of a number. Prototypes #include <math.h> double sin(double x); float sinf(float x); long double sinl(long double x); Description Calculates the sine of the value x, where x is in radians. For those of you who don't remember, radians are another way of measuring an angle, just like degrees. To convert from degrees to radians or the other way around, use the following code: degrees = radians * 180.0f / M_PI; radians = degrees * M_PI / 180; Return Value Returns the sine of x. The variants return different types. Example double sinx; long double ldsinx; sinx = sin(3490.0); // round and round we go! ldsinx = sinl((long double)3.490); See Also cos(), tan(), asin() Beej's Guide to C Programming 125 15.2. cos(), cosf(), cosl() Calculate the cosine of a number. Prototypes #include <math.h> double cos(double x) float cosf(float x) long double cosl(long double x) Description Calculates the cosine of the value x, where x is in radians. For those of you who don't remember, radians are another way of measuring an angle, just like degrees. To convert from degrees to radians or the other way around, use the following code: degrees = radians * 180.0f / M_PI; radians = degrees * M_PI / 180; Return Value Returns the cosine of x. The variants return different types. Example double sinx; long double ldsinx; sinx = sin(3490.0); // round and round we go! ldsinx = sinl((long double)3.490); See Also sin(), tan(), acos() Beej's Guide to C Programming 126 15.3. tan(), tanf(), tanl() Calculate the tangent of a number. Prototypes #include <math.h> double tan(double x) float tanf(float x) long double tanl(long double x) Description Calculates the tangent of the value x, where x is in radians. For those of you who don't remember, radians are another way of measuring an angle, just like degrees. To convert from degrees to radians or the other way around, use the following code: degrees = radians * 180.0f / M_PI; radians = degrees * M_PI / 180; Return Value Returns the tangent of x. The variants return different types. Example double tanx; long double ldtanx; tanx = tan(3490.0); // round and round we go! ldtanx = tanl((long double)3.490); See Also sin(), cos(), atan(), atan2() Beej's Guide to C Programming 127 15.4. asin(), asinf(), asinl() Calculate the arc sine of a number. Prototypes #include <math.h> double asin(double x); float asinf(float x); long double asinl(long double x); Description Calculates the arc sine of a number in radians. (That is, the value whose sine is x.) The number must be in the range -1.0 to 1.0. For those of you who don't remember, radians are another way of measuring an angle, just like degrees. To convert from degrees to radians or the other way around, use the following code: degrees = radians * 180.0f / M_PI; radians = degrees * M_PI / 180; Return Value Returns the arc sine of x, unless x is out of range. In that case, errno will be set to EDOM and the return value will be NaN. The variants return different types. Example double asinx; long double ldasinx; asinx = asin(0.2); ldasinx = asinl((long double)0.3); See Also acos(), atan(), atan2(), sin() Beej's Guide to C Programming 128 15.5. acos(), acosf(), acosl() Calculate the arc cosine of a number. Prototypes #include <math.h> double acos(double x); float acosf(float x); long double acosl(long double x); Description Calculates the arc cosine of a number in radians. (That is, the value whose cosine is x.) The number must be in the range -1.0 to 1.0. For those of you who don't remember, radians are another way of measuring an angle, just like degrees. To convert from degrees to radians or the other way around, use the following code: degrees = radians * 180.0f / M_PI; radians = degrees * M_PI / 180; Return Value Returns the arc cosine of x, unless x is out of range. In that case, errno will be set to EDOM and the return value will be NaN. The variants return different types. Example double acosx; long double ldacosx; acosx = acos(0.2); ldacosx = acosl((long double)0.3); See Also asin(), atan(), atan2(), cos() Beej's Guide to C Programming 129 15.6. atan(), atanf(), atanl(), atan2(), atan2f(), atan2l() Calculate the arc tangent of a number. Prototypes #include <math.h> double atan(double x); float atanf(float x); long double atanl(long double x); double atan2(double y, double x); float atan2f(float y, float x); long double atan2l(long double y, long double x); Description Calculates the arc tangent of a number in radians. (That is, the value whose tangent is x.) The atan2() variants are pretty much the same as using atan() with y/x as the argument .except that atan2() will use those values to determine the correct quadrant of the result. For those of you who don't remember, radians are another way of measuring an angle, just like degrees. To convert from degrees to radians or the other way around, use the following code: degrees = radians * 180.0f / M_PI; radians = degrees * M_PI / 180; Return Value The atan() functions return the arc tangent of x, which will be between PI/2 and -PI/2. The atan2() functions return an angle between PI and -PI. Example double atanx; long double ldatanx; atanx = atan(0.2); ldatanx = atanl((long double)0.3); atanx = atan2(0.2); ldatanx = atan2l((long double)0.3); See Also tan(), asin(), atan() Beej's Guide to C Programming 130 15.7. sqrt() Calculate the square root of a number Prototypes #include <math.h> double sqrt(double x); float sqrtf(float x); long double sqrtl(long double x); Description Computes the square root of a number. To those of you who don't know what a square root is, I'm not going to explain. Suffice it to say, the square root of a number delivers a value that when squared (multiplied by itself) results in the original number. Ok, fine--I did explain it after all, but only because I wanted to show off. It's not like I'm giving you examples or anything, such as the square root of nine is three, because when you multiply three by three you get nine, or anything like that. No examples. I hate examples! And I suppose you wanted some actual practical information here as well. You can see the usual trio of functions here--they all compute square root, but they take different types as arguments. Pretty straightforward, really. Return Value Returns (and I know this must be something of a surprise to you) the square root of x. If you try to be smart and pass a negative number in for x, the global variable errno will be set to EDOM (which stands for DOMain Error, not some kind of cheese.) Example // example usage of sqrt() float something = 10; double x1 = 8.2, y1 = -5.4; double x2 = 3.8, y2 = 34.9; double dx, dy; printf("square root of 10 is %.2f\n", sqrtf(something)); dx = x2 - x1; dy = y2 - y1; printf("distance between points (x1, y1) and (x2, y2): %.2f\n", sqrt(dx*dx + dy*dy)); And the output is: square root of 10 is 3.16 distance between points (x1, y1) and (x2, y2): 40.54 See Also hypot() 131 16. Complex Numbers . 122 15. Mathematics It's your favorite subject: Mathematics! Hello, I'm Doctor Math, and I'll