Symbolic rewriting of trigonometric functions with a exponential function.

I use MATLAB2023a with symbolic math toolbox.

I want to rewrite a symbolic equation by summing several cosine and sine terms.

How can I make use of the following rule in MATLAB?

Specifically, I want to combine cos and sin in the following code.

clear; clc;
syms y(t);
eqn = y(t) == 0.00225*exp(-5.0*t)*(71.0*cos(8.11*t) + 43.8*sin(8.11*t))

eqn = 

rewrite(eqn, 'sincos') %% failed :(

ans = 

simplify(eqn) %% failed :(

ans = 

combine(eqn) %% failed :(

ans = 

Thank you in advance.

Answer 1

[Dyuman Joshi]

rewrite() does not produce the following conversion.

You can do the following -

syms t
%Define expressions separately
y1 = (71.0*cos(8.11*t) + 43.8*sin(8.11*t));
y2 = 0.00225*exp(-5.0*t);

%rewrite the sum of sin and cos using combine()
out = combine(y1,'sincos')

out = 

%multiply the expressions to get the final/desired output
fun = y2*out

fun =