Inverse Functions in Math

[a.dheeraj.kumar]

i know that there is a function to find the logarithm of a number, sin,
cos, tan etc. but are there which can find sin^-1, cos^-1, tan^-1 and
antilog of a given number?

PS: sin^-1 means sin inverse. eg:
if sin 30 =1/2
30=sin inverse of 1/2

HELP!

 

[Dik T. Winter]

> i know that there is a function to find the logarithm of a number, sin,
> cos, tan etc. but are there which can find sin^-1, cos^-1, tan^-1 and
> antilog of a given number?
>
> PS: sin^-1 means sin inverse. eg:
> if sin 30 =1/2
> 30=sin inverse of 1/2

asin, acos, atan and exp.

 

[a.dheeraj.kumar]

thanks man, i understood all functions except exp function.

can you tell me how to use this function to find the antilog of
0.something to base 10, and also how to make it work for different bases

 

[REH]

thanks man, i understood all functions except exp function.

can you tell me how to use this function to find the antilog of
0.something to base 10, and also how to make it work for different bases

The exp function is just like the pow function but with a constant base,
namely e. If you want "exp" with 10 or other bases, use pow.

REH

 

[Walter Roberson]

thanks man, i understood all functions except exp function.

can you tell me how to use this function to find the antilog of
0.something to base 10, and also how to make it work for different bases

(Using non-C notation in this portion)

Log{N}[x] -> ln[x] / ln[N]

so

ln[x] -> Log{N}[x] * ln[N]

so

exp[ln[x]] -> exp[ Log{N}[x] * ln[N] ]

hence

x -> exp[ Log{N}[x] * ln[N] ]

Hence, to find the antilog of something base 10, Y, take
(using C notation)

exp(Y * log(10.))


For example, log10(1000.) = 3., ln(10.) ~= 2.3025851, and
exp( 3. * 2.3025851 ) = exp( 6.9077553 ) ~= 1000.0

 

[Rouben Rostamian]

Hence, to find the antilog of something base 10, Y, take
(using C notation)

exp(Y * log(10.))

Or simply:

pow(10., Y)

 

[CBFalconer]

i know that there is a function to find the logarithm of a number, sin,
cos, tan etc. but are there which can find sin^-1, cos^-1, tan^-1 and
antilog of a given number?

PS: sin^-1 means sin inverse. eg:
if sin 30 =1/2
30=sin inverse of 1/2

Such as arcsin or asin, and exp?

 

[Martin Ambuhl]

thanks man, i understood all functions except exp function.

can you tell me how to use this function to find the antilog of
0.something to base 10, and also how to make it work for different bases

pow(base, x) == exp(x * log(base)) :


#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <float.h>
#include <time.h>


int main(void)
{
double x, y;
int i;
double M_log10 = log(10);
srand(time(0));

printf("exp(x) is the antilog(x, base=%.*g)\n\n", DBL_DIG, exp(1));

for (i = 0; i < 10; i++) {
x = rand() / (1. + RAND_MAX);
y = exp(x),
printf("exp(%g) = %g, log(%g) = %g\n", x, y, y, log(y));
y = pow(10, x);
printf("pow(10, %g) = %g, log10(%g) = %g\n", x, y, y, log10(y));
y = exp(x * M_log10);
printf("exp(%g * log(10)) = %g, log10(%g) = %g\n\n",
x, y, y, log10(y));
}
return 0;
}


This is the result of one run:

exp(x) is the antilog(x, base=2.71828182845905)

exp(0.540308) = 1.71654, log(1.71654) = 0.540308
pow(10, 0.540308) = 3.46983, log10(3.46983) = 0.540308
exp(0.540308 * log(10)) = 3.46983, log10(3.46983) = 0.540308

exp(0.655142) = 1.92542, log(1.92542) = 0.655142
pow(10, 0.655142) = 4.52004, log10(4.52004) = 0.655142
exp(0.655142 * log(10)) = 4.52004, log10(4.52004) = 0.655142

exp(0.430014) = 1.53728, log(1.53728) = 0.430014
pow(10, 0.430014) = 2.69162, log10(2.69162) = 0.430014
exp(0.430014 * log(10)) = 2.69162, log10(2.69162) = 0.430014

exp(0.656084) = 1.92723, log(1.92723) = 0.656084
pow(10, 0.656084) = 4.52985, log10(4.52985) = 0.656084
exp(0.656084 * log(10)) = 4.52985, log10(4.52985) = 0.656084

exp(0.567552) = 1.76394, log(1.76394) = 0.567552
pow(10, 0.567552) = 3.69447, log10(3.69447) = 0.567552
exp(0.567552 * log(10)) = 3.69447, log10(3.69447) = 0.567552

exp(0.346806) = 1.41454, log(1.41454) = 0.346806
pow(10, 0.346806) = 2.22232, log10(2.22232) = 0.346806
exp(0.346806 * log(10)) = 2.22232, log10(2.22232) = 0.346806

exp(0.418147) = 1.51914, log(1.51914) = 0.418147
pow(10, 0.418147) = 2.61907, log10(2.61907) = 0.418147
exp(0.418147 * log(10)) = 2.61907, log10(2.61907) = 0.418147

exp(0.859071) = 2.36097, log(2.36097) = 0.859071
pow(10, 0.859071) = 7.22888, log10(7.22888) = 0.859071
exp(0.859071 * log(10)) = 7.22888, log10(7.22888) = 0.859071

exp(0.824404) = 2.28052, log(2.28052) = 0.824404
pow(10, 0.824404) = 6.67427, log10(6.67427) = 0.824404
exp(0.824404 * log(10)) = 6.67427, log10(6.67427) = 0.824404

exp(0.225011) = 1.25234, log(1.25234) = 0.225011
pow(10, 0.225011) = 1.67885, log10(1.67885) = 0.225011
exp(0.225011 * log(10)) = 1.67885, log10(1.67885) = 0.225011