[itex]L[sin(at)]=\frac{a}{s^{2}+a^{2}}, Re>0[/itex](adsbygoogle = window.adsbygoogle || []).push({});

[itex]L[e^{kt}]=\frac{1}{s-k}, s>k[/itex]

[itex]L[e^{-kt}]=\frac{1}{s+k}, s<-k[/itex]

[itex]L[sin(at)]=\frac{1}{2i}L[e^{iat}-e^{-iat}][/itex]

[itex]=\frac{1}{2i}L[e^{iat}]-L[e^{-iat}][/itex]

Using the above relations

[itex]=\frac{1}{2i}[\frac{1}{s-ia}-\frac{1}{s+ia}], s>ia, s<-ia[/itex]

The problem is that I don't understand, howands>iacould imply that Real part of s>0?s<-ia

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Laplace Sine Transform

**Physics Forums | Science Articles, Homework Help, Discussion**