Trigonometric and Hyperbolic Functions

f$\left(\vphantom{ t}\right.$t$\left.\vphantom{ t}\right)$ F$\left(\vphantom{ s}\right.$s$\left.\vphantom{ s}\right)$ = L$\left\{\vphantom{ f}\right.$f$\left.\vphantom{ f}\right\}$$\left(\vphantom{ s}\right.$s$\left.\vphantom{ s}\right)$
sin kt sinh kt ${\dfrac{{2k^{2}s}}{{s^{2}+4k^{4}}}}$


sin kt cosh kt ${\dfrac{{k\left( s^{2}+2k^{2}\right) }}{{s^{4}+4k^{4}}}}$


cos kt sinh kt ${\dfrac{{k\left( s^{2}-2k^{2}\right) }}{{s^{4}+4k^{4}}}}$


cos kt cosh kt     ${\dfrac{{s^{3}}}{{s^{4}+4k^{4}}}}$