Symbolic rewriting of trigonometric functions with a exponential function.
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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))
rewrite(eqn, 'sincos') %% failed :(
simplify(eqn) %% failed :(
combine(eqn) %% failed :(
Thank you in advance.
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Accepted Answer
Dyuman Joshi
on 22 May 2023
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')
%multiply the expressions to get the final/desired output
fun = y2*out
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