Find L{f(t)} by first using an appropriate trigonometric identity. L is the symbol for Laplace transformation. f(t)=sin(2t)cos(2t) Laplace transform equation: L{f(t)}=int_0^infty e^(-st)f(t)dt

Bernard Boyer 2022-07-30 Answered
Find L{f(t)} by first using an appropriate trigonometric identity. L is the symbol for Laplace transformation.
f ( t ) = sin ( 2 t ) cos ( 2 t )
Laplace transform equation: L { f ( t ) } = 0 e s t f ( t ) d t
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Rihanna Robles
Answered 2022-07-31 Author has 18 answers
A good trick here is to use a trig identity to separate your f(t) into a simple form.
sin ( 2 t ) + cos ( 2 t ) = 1 / 2 sin ( 2 t + 2 t ) + 1 / 2 sin ( 2 t 2 t ) = 1 / 2 sin ( 4 t )
Now, you can plug this into your integral. To double check your answer you can use the table of laplace transforms, you canfind this anywhere on the internet, just google it. and from there you can easy convert things into laplace domain, provided you have them in the correct form.
so L 1 / 2 s i n ( 4 t ) = 1 / 2 4 / ( s 2 + 4 2 )
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

New questions