What is laplacetransform sin(3t)cos(3t) ?

The answer to laplacetransform sin(3t)cos(3t) is 3/(s^2+36)

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laplacetransform sin(3t)cos(3t)

laplace transform

sin (3 t) cos (3 t)

\frac{3}{s ^{2} + 36}

Solution steps

L {sin (3 t) cos (3 t)}

Rewrite using trig identities

L {\frac{1}{2} sin (6 t)}

Use the constant multiplication property of Laplace Transform:

For function

f (t)

and constant

a : L {a \cdot f (t)} = a \cdot L {f (t)}

= \frac{1}{2} L {sin (6 t)}

L {sin (6 t)} : \frac{6}{s ^{2} + 36}

= \frac{1}{2} \cdot \frac{6}{s ^{2} + 36}

Refine

\frac{1}{2} \frac{6}{s ^{2} + 36} : \frac{3}{s ^{2} + 36}

= \frac{3}{s ^{2} + 36}

f (x) = \frac{1}{2 x}, at x = 1

2 y^{^{''}} + 11 y^{^{'}} - 6 y = 0

\frac{d y}{d x} = \frac{y}{x ^{3} + 3 x ^{2} + 2 x}

f (x) = ln (1 + sin (\frac{4}{x ^{2}}))

y = sin (4 x) + sin^{2} (4 x), (0, 0)

What is laplacetransform sin(3t)cos(3t) ?
The answer to laplacetransform sin(3t)cos(3t) is 3/(s^2+36)