How to calculate the coefficients of non-polynomial terms

I am trying to find the coefficients of non-polynomial terms

For example

syms x
a=-9*cos(x)*4+x*9+4*sin(x)

I want to find the coefficients of sin(x) and cos(x).

When using coeffs its not working

Thanks

Answer 1

[madhan ravi]

syms x
a=-9*cos(x)*4+x*9+4*sin(x)

[C,T] = coeffs(a) %edited after John’s comment.

It’s working for me

[John D'Errico]

+1. Yep. For me too.

coeffs(a)
ans =
[ 4, -36, 9]

I wonder of the OP has an older release of MATLAB? coeffs was introduced before R2006a, so is pretty old.

Perhaps more likely, is the problem that it returns those coefficients in a surprising order?

a
a =
9*x - 36*cos(x) + 4*sin(x)

I recall that the order of terms in such an expression need not be what you think. If you want to be sure which order you got, you can use the two return argument form for coeffs.

[C,T] = coeffs(a)
C =
[ 9, -36, 4]
T =
[ x, cos(x), sin(x)]

[madhan ravi]

Thank you @John D’Errico. Make sure you have the symbolic toolbox @T.S.Singh.

[Image Analyst]

I don't have the symbolic toolbox, but if the terms are -9*cos(x)*4 + x*9 + 4*sin(x), why aren't the coefficients

[-9*4, 9, 4] = [-36, 9, 4]

The cos() has two coefficients -9 and 4, the x has one coefficient (9), and the sin() has one coefficient, 4.

And what would be the coefficients if the x inside the cos() or sin() also had a coefficient, like 36*cos(5x) + 7*sin(2*pi*x)?

[madhan ravi]

@sir Image Analyst (tried your latter example)it didn’t return the argument as coefficient (tried my edited answer) but it returned T as cos(5*x) and sin(2*pi*x) and C as 36 and 7 . Because they are arguments of the function and not the coefficients.

[Image Analyst]

T S, you haven't said what YOU got for C and T and why it's different than the answers John and madhan got. Please state what you got, and what you expected, keeping in mind that the order may be rearranged like John said.

[T S Singh]

@Image Analyst I got [ 9, -36, 4]

[T S Singh]

@madhan ravi What suppose the coefficients has other symbolic terms, say

syms x y
a=-9*y*cos(x)*4+x*9+4*sin(x);
[C,T] = coeffs(a)
% C =[ 9, -36, 4]
% T =[ x, y*cos(x), sin(x)]

Its returning only the numeric value and when I specify the variable

[C,T] = coeffs(a,x)
% C =[ 9, 4*sin(x) - 36*y*cos(x)]
% T =[ x, 1]

Is there any other possible way?

[John D'Errico]

Ok, if you specifically want the coefficients of specific terms, you can use coeffs, like this:

[C,T] = coeffs(a,{sin(x),cos(x)})
C =
[ 4, -36, 9*x]

T =
[ sin(x), cos(x), 1]

So C(1) is the coefficient of sin(x), C(2) is the coefficient of cos(x).

a
a =
9*x - 36*cos(x) + 4*sin(x)

Is this what you are looking to find? I'm not really sure what you are asking in your last comment.

[madhan ravi]

Try this @T S SINGH:

syms x y
a=-9*y*cos(x)*4+x*9+4*sin(x);
[C,T] = coeffs(a,[x y])

also familiarise more about coeffs

[T S Singh]

Yes, Actually I have included a new symbol y in the expression

syms x y
a=-9*y*cos(x)*4+x*9+4*sin(x);
[C,T] = coeffs(a,{sin(x),cos(x),x})

C =

[ 4, -36*y, 9]

T =

[ sin(x), cos(x), x]

Thanks John

[madhan ravi]

if you find it useful please accept the answer, thank you @John