Extracting coefficients of 'sinwt', 'coswt', sin2wt etc from a symbiolic expression.

Hello,

I am having a mathmatical symbolic expression and want to extract the coefficient of 'sinwt', 'coswt', 'sin2wt' and so on.

For e.g. the expression is,

where, , and are symbolic variables. Now, is there anyway to get the coefficient of 'sinwt', 'coswt', 'cos3wt' etc. from this expression ? or in other words, is it possible to get the following desired output ?

[Walter Roberson]

What would be the desired output in that example? What would be the desired output for the example of

[Yugal Gupta]

The desired output of this example is,

[Walter Roberson]

The origin of your cos(3*omega*t) and the division by 2 is not obvious to me. I do find that,

syms k [1 3]
syms omega t
y = k(1)*sin(omega*t) * k(2)*sin(2*omega*t) + k(3) * sin(omega*t)

y = 

yexp = rewrite(y, 'exp')

yexp = 

yexps = simplify(yexp)

yexps = 

ysincos = rewrite(yexps, 'sincos')

ysincos = 

ysincoss = simplify(ysincos)

ysincoss = 

[Yugal Gupta]

In the end, I added the following code and it gives me the desired output.

combine(ysincoss,'sincos')

[Walter Roberson]

Ah... you can get there in a single step with

combine(y, 'sincos')

Answer 1

[Gargi Patil]

Hi,

My understanding is that you would like to extract the coefficients of a symbolic trigonometric expression. The function "coeffs" can be used to return coefficients of an expression with respect to a specified term as follows:

syms a b c x 
expr = a*sin(x)*b*sin(2*x) + c*sin(x);
[csin, tsin] = coeffs(expr, [sin(x), sin(2*x)])

csin = 

tsin = 

[Walter Roberson]

It turned out that they wanted the express rewritten in terms of cos(), and were not looking for coefficients such as you get with coeffs(); see https://www.mathworks.com/matlabcentral/answers/894797-extracting-coefficients-of-sinwt-coswt-sin2wt-etc-from-a-symbiolic-expression#comment_1679322