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The ArcCos of radical[3]/2 is .5235987756, which is pi/6. But suppose I didn't know that. My question is how do I convert these kinds of decimal values to radians? If I could, I would like to know how to do it with: TI-83 Plus calculator, how to do it with Mathematica 4.2, and also by hand, if it's possible, thanks. (The problem that led me to ask this: ArcTan of 170/150radical[3])

I appreciate any help

I appreciate any help

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For instance : ".5235987756 rad" is such a measure, "12.5 deg" also is, and "99.05 grad" is too.

Are you looking for some algorythm that would do .5235987756 --> pi/6 automatically ?

In the negative, you already have what you're looking for. You just need to make sure that the calculator you're using is in the correct mode. Even the windows calc applet has such a setting (in scientific mode).

Q

--------------------------

2 * 3.141592653589793238462643

This is the angular fractional percentage of the unit circle.

#include <stdio.h>

#include <math.h>

#define HiSearchLimit 100

int main( int argc, char * argv )

{

double err, target, pi, miss;

int num, den, up,down;

pi = 3.1415926;

target = 0.5235987756;

err = 99999999.9; up = 0; down = 0;

for( num = HiSearchLimit; num >= 1; num-- )

for( den = HiSearchLimit; den >= 1; den-- ) {

miss = fabs( (pi * ( (double) num / (double) den )) - target );

if( miss <= err ) { err = miss; up = num; down = den; }

}

if( down == 0 ) printf("No approx???\n");

else

printf("closest approx is pi * %d / %d\n", up, down );

}

Q = 0.5235987756

Qp = Q / pi = Q / 3.141592653589793238462643

16667

= ----------

100000

You would then prime-factoriize both numerator and denominator and cancel like factors. You would then be left with a rational number which is a (in this case 5-decimal)

approximation to) pi-multiplier roughly equivalent to your original angle Q.

As you can see, however, the more decimal places you keep, the more factorization becomes computationally expensive.

The TI-83, 85, 86 do not do symbolic manipulation and hence do not have this feature.

If your calculator is set to degree mode, the result should be 30. If it is in radian mode, then the result is 0.5235987756 (rounded). If you wish to apply a number (in radians) to the unit circle, convert it to degrees.

0.5235987756 * 180 / Pi = 30.00000000 (rounded)

You then have to decide for yourself whether 30.000... is 30.

Mathematica operates similarly to the TI-89, 92 as it does symbolic manipulation.

Bradley

i.e. pi, pi/2, pi/3, pi/4, pi/6, 2pi/3 and so on. (Mind the tolrance in the conversion). No use even bothering with trying to display 1365653/3233392 pi radians, the decimal number will probaby do the job if you cant find it in your table.

This is of course if your answer comes in the form .332323rad, in mathematica you could probably do symbolics all the way, and just avoid the last step where the output converts the answer to decimal. Mathematica of also easily also does decimal to fraction conversion like mrdtn mentioned above, but

be aware that fractions are NOT easily readable unless among the really easy ones, pi/2 etc.

Conclusion:

If the result should be read by humans, I'd go for the small table with fallback to decimals. If the result is to be used in further calculations, I'd go with either trying to persuade mathematica to do symbols all the way, or tell it to convert to fractions.

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