[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

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# Laplace Sine Transform

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