What is laplacetransform sin(6(t-pi/6)) ?

The answer to laplacetransform sin(6(t-pi/6)) is -6/(s^2+36)

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laplacetransform sin(6(t-pi/6))

laplace transform

sin (6 (t - \frac{π}{6}))

- \frac{6}{s ^{2} + 36}

Solution steps

L {sin (6 (t - \frac{π}{6}))}

Use Laplace Transform table:

L {sin (a t + b)} = \frac{s \cdot sin ( b ) + a \cdot cos ( b )}{s ^{2} + a ^{2}}

L {sin (6 (t - \frac{π}{6}))} = \frac{s sin ( - π ) + 6 cos ( - π )}{s ^{2} + 6 ^{2}}

= \frac{s sin ( - π ) + 6 cos ( - π )}{s ^{2} + 6 ^{2}}

= - \frac{6}{s ^{2} + 36}

y = \frac{t}{( t - 4 ) ^{2}}

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} + 4 y = sin (x)

n = 0 \sum \infty \frac{1}{( 4 n + 3 ) ^{2}}

\frac{d}{d x} ((x + 3)^{\frac{1}{2}})

\frac{d x}{d y} = x + y

What is laplacetransform sin(6(t-pi/6)) ?
The answer to laplacetransform sin(6(t-pi/6)) is -6/(s^2+36)