how to get precise conversion in matlab?

hi

when i want to convert degrees(89.999999999999668207879992402105) into radians matlab gives 1.5707963267948966192313216916398 value as a output. but when i reverse the process it gives round off figure 90. but i need actual and accurate conversion value not the round off.*

vpa(89.999999999999668207879992402105*pi/180)

ans = 1.5707963267948966192313216916398

but when re-convert back to original form

vpa(1.5707963267948966192313216916398*180/pi)

ans =  90.0

i also change the the number of digits like vpa(1.5707963267948966192313216916398*180/pi,100) etc but observe the same results. kindly help me i will be highly thankful to you for this act of kindness

with best regards mudasir ahmed

Answer 1

[Walter Roberson]

Every time you use a literal number in MATLAB that is not inside a string, MATLAB is going to evaluate the number as double precision before the Symbolic toolbox gets control. You need to quote your numbers. You should also get in the habit of sym()'ing them

vpa('89.999999999999668207879992402105*pi/180')
vpa('1.5707963267948966192313216916398*180/pi')

but better

vpa(sym('89.999999999999668207879992402105*pi/180'))
vpa(sym('1.5707963267948966192313216916398*180/pi'))

[Mudasir Ahmed]

dear sir

Thanks for valuable information, but i have a Array of 100 by 3 values, will this format convert the whole array (variable).

vpa(sym('array*180/pi'))

[Walter Roberson]

Code the array as text and call sym() on each element of the text.

Note: in the above you had a problem because you attempted to take the text version of the ans as numeric input. If you had assigned the answer to a variable you would not have a problem.

PI = sym('pi');

in_val = sym('89.999999999999668207879992402105');
as_rad = vpa(in_val*PI/180);
as_deg = vpa(as_rad * 180 / PI);

Note: R2015b introduces deg2rad() and rad2deg() but I am not certain that it would handle symbolic values with sufficient precision of Pi.

[Mudasir Ahmed]

Dear sir,

i have to to do like below

    a=vpa([[sym(a1) sym(a2) sym (a3)];[sym(a4) sym(a5) sym (a6)];...[sym(a298) sym(a299) sym (a300)].
  for i=1:100
  forj=1:3
  b(i,j)=a(i,j)*pi/180
  end
  end

Sir it seems lengthy and manual work if large array size is considered. so is there any automatic process or procedure.

[Walter Roberson]

No, if your a1 and a2 and so on are already extended precision then they must already be symbolic and applying sym() to them would not be needed.

If your values are not already extended precision then it does not make mathematical sense to do an extended precision calculation of radians. But in such a case you could do

a = [a1 a2 a3 ... a300];
b = sym(a) * sym('pi') / 180;

[Walter Roberson]

Where are those numbers coming from? What is class(angles) ?

As far as double precision numbers are concerned, 89.999999999999667479426986067257 and 89.999999999999668207879992402105 are the same number, both of them being 89.9999999999996731503415503539144992828369140625 . That is something that cannot be changed with double precision numbers. You need to use some kind of extended precision numbers if you want them to be different, and using extended precision numbers will require a different syntax to enter the numbers.

angles= [    
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[Mudasir Ahmed]

thank you so much sir :)