Question

Find script l{f(t)} by first using a trigonometric identity. (write your answer as a function of s.) f(t) = sin 6t cos 6t

Answer 1

∵ f(t) = sin 6t cos 6t = (0.5) * 2 sin 6t cos 6t
∴ f(t) = 0.5 sin 12t

∵
`l(sin \ at) = (a)/( s^(2) +a^2)`
∴
`l[f(t)] = l (0.5 \ sin \ 12t) = 0.5* (12)/(s^2+12^2) = (6)/(s^2+144)`