Question Number 135823 by Khakie last updated on 16/Mar/21
$${how}\:{can}\:{this}\:{be}\:{equal}??? \\ $$$${sin}\:{wt}\:\:=\:{e}^{−{at}} \: \\ $$$$ \\ $$
Commented by mr W last updated on 16/Mar/21
$${why}\:{not}? \\ $$$$−\mathrm{1}\leqslant\mathrm{sin}\:{wt}\leqslant\mathrm{1} \\ $$$${if}\:{a}>\mathrm{0},\:{e}^{−{at}} <\mathrm{1}\:{when}\:{t}>\mathrm{0}\:\Rightarrow\:{there} \\ $$$${exists}\:{t}>\mathrm{0}\:{such}\:{that}\:\mathrm{sin}\:{wt}={e}^{−{at}} \\ $$$${if}\:{a}<\mathrm{0},\:{e}^{−{at}} <\mathrm{1}\:{when}\:{t}<\mathrm{0}\:\Rightarrow\:{there} \\ $$$${exists}\:{t}<\mathrm{0}\:{such}\:{that}\:\mathrm{sin}\:{wt}={e}^{−{at}} \\ $$
Commented by mr W last updated on 16/Mar/21
Commented by Khakie last updated on 17/Mar/21
$${thanks} \\ $$