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

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.

Thanks in advance.

cos(pi/2)

ans = 6.1232e-17

syms a
a*cos(pi/2)

ans = 

[Torsten]

You work with cosd. For cosd, cosd(90) = 0, not cosd(pi/2).

[Mohd Aaquib Khan]

I am using cos(pi/2)*k1 as you can find in the second screenshot.

Also, Are the screenshots I have added visible? I am unable to see those now.

[Torsten]

I could only see your screenshots after I opened your contribution using "Edit".

[Mohd Aaquib Khan]

I fixed it now, this below is what I meant

cos(pi/2)

ans = 6.1232e-17

syms a
a*cos(pi/2)

ans = 

Answer 1

[Walter Roberson]

The answer you are looking for is

digits(4)
sympref('FloatingPointOutput',true);

However, I do not recommend this.

[Mohd Aaquib Khan]

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 = 

Answer 2

[Steven Lord]

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]

Thank you, yes vpa and sympref are both working fine and that is what I wanted.

Answer 3

[Paul]

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

[Mohd Aaquib Khan]

Ok cos(90) works this way thanks, but with other angles it is still showing the same.

phi = [50, 25, 30 90]';
syms a
cosd(sym(phi))*a

ans = 

eval(cosd(sym(phi))*a)

ans = 

[Torsten]

For phi = 30 and phi = 90, cos(phi) is correctly simplified.

What would you expect for cos(50) and cos(25) ? I don't see a simple representation.

[Walter Roberson]

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.