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

∵ $l(sin \ at) = \frac{a}{ s^{2} +a^2}$
∴$l[f(t)] = l (0.5 \ sin \ 12t) = 0.5* \frac{12}{s^2+12^2} = \frac{6}{s^2+144}$