# Question:Conversion from complex exponentials to simple trig functions

## Question:Conversion from complex exponentials to simple trig functions

Maple
I'm trying to put together an analysis of a damped harmonic oscillator for a tutorial and I can't get the answer into the form I'd like. If you have a complex exponential, you can easily express it as a sum of a sin and cos using the convert function with the 'trig' option. If you have a term in the exponent that always evaluates to complex value because of the assumptions on your variables, however, it will always write the expression in terms of sinh and cosh. Is there any way to force Maple to put the solution in terms of sin and cos?

assume(xi::real);
getassumptions(xi);
{xi::(RealRange(Open(0), Open(1)))}
convert(A*exp(-sqrt(0.1-1)*t), trig);
A (cos(0.9486832981 t) - I sin(0.9486832981 t))
convert(A*exp(-sqrt(xi^2-1)*t), trig);
/ / (1/2) \ / (1/2) \\
| |/ 2 \ | |/ 2 \ ||
A \cosh\\xi - 1/ t/ - sinh\\xi - 1/ t//
is((sqrt(xi^2-1))::real);
FAIL
is((sqrt(xi^2-1))::imaginary);
true

Thanks,

Kevin
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