# How to fix the large and mad fractions when dealing with symbolic vars

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Mohd Aaquib Khan on 18 Sep 2022
Commented: Mohd Aaquib Khan on 19 Sep 2022
Hi guys,
I face this often, as you can see below that cos(phi) and cos(psi) are decent entities, but when they are used with a symbolic variable (kn here), it shows huge fractions. Is there an easy way to make the coefficients of k1 k2 and k3 in the short format or some decent fractions.
Even something as trivial as k1*cos(pi/2) is not evaluated to be 0 as shown below. I fear that this leads to truncation errors.
cos(pi/2)
ans = 6.1232e-17
syms a
a*cos(pi/2)
ans =
Mohd Aaquib Khan on 18 Sep 2022
I fixed it now, this below is what I meant
cos(pi/2)
ans = 6.1232e-17
syms a
a*cos(pi/2)
ans =

Walter Roberson on 19 Sep 2022
The answer you are looking for is
digits(4)
sympref('FloatingPointOutput',true);
However, I do not recommend this.
Mohd Aaquib Khan on 19 Sep 2022
Yes thank you, vpa() also works fine for the same result.
phi = [50, 25, 30 90]';
syms a
vpa(cosd(phi)*a,4)
ans =
digits(4)
sympref('FloatingPointOutput',true);
phi = [50, 25, 30 90]';
cosd(phi)*a
ans =

Steven Lord on 18 Sep 2022
Symbolically, use vpa or double or use the sympref function to change the FloatingPointOutput preference.
Numerically, if you want to compute the sine or cosine of an angle expressed as a multiple of pi, use sinpi or cospi respectively.
format longg
[sin(0.5*pi), cos(0.5*pi); sinpi(0.5), cospi(0.5)]
ans = 2×2
1 6.12323399573677e-17 1 0
Mohd Aaquib Khan on 19 Sep 2022
Thank you, yes vpa and sympref are both working fine and that is what I wanted.

Paul on 18 Sep 2022
In this expression
syms a
a * cos(pi/2)
ans =
the cos() is evaluated numerically and the result converted to a sym to multiply with a. The numerical cos(pi/2) is not zero.
Force the cos to be evaluated symbolically
a * cos(pi/sym(2))
ans =
0
or
a * cos(sym(pi)/2)
ans =
0
Walter Roberson on 19 Sep 2022
You should never eval() a symbolic expression. eval() of a symbolic expression is not documented by Mathworks. In practice it is treated as eval(char()) of the expression. However, char() of a symbolic expression is written in a mix of MATLAB, English, and the internal MuPAD programming language, and is not generally something that can be computed.

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