diffrential equations

Question

Find ℒ{f(t)}

 

by first using a trigonometric identity. (Write your answer as a function of s.)

f(t) = sin(5t + 6)

Answer 1

f(t) = sin(5t)cos6 + cos(5t)sin6.

So L{f(t)} = cos6·5/(s² + 25) + sin6·s/(s² + 25)= (5cos6 + s·sin6)/(s² + 25)·