# Laplace transform

• Nov 25th 2009, 10:17 AM
Provoke
Laplace transform
Hi,

I'm trying to find the laplace transform of the following function:

f(t) = cos(at+b)

I'm having trouble with eulers identity:

I know exp(iat) = cos(at) + isin(at)
I don't know if exp(iat+b) = cos(at+b) + isin(at+b)

thx 4 help
• Nov 25th 2009, 10:31 AM
Provoke
I calculated as if what I said earlier was true, I get:

sexp(b) / (s^2+a^2)

can anyone confirm? thx
• Nov 26th 2009, 03:15 AM
mr fantastic
Quote:

Originally Posted by Provoke
Hi,

I'm trying to find the laplace transform of the following function:

f(t) = cos(at+b)

I'm having trouble with eulers identity:

I know exp(iat) = cos(at) + isin(at)
I don't know if exp(iat+b) = cos(at+b) + isin(at+b)

thx 4 help

$\cos (at + b) = \frac{1}{2} \left( e^{i(at + b)} + e^{-i(at + b)}\right)$.

Quote:

Originally Posted by Provoke
I calculated as if what I said earlier was true, I get:

sexp(b) / (s^2+a^2)

can anyone confirm? thx

This is not correct. The correct answer is $\frac{s \cos (b) - a \sin (b)}{s^2 + a^2}$.