What is laplacetransform sin(6(t-(3pi)/6)) ?

The answer to laplacetransform sin(6(t-(3pi)/6)) is -6/(s^2+36)

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laplacetransform sin(6(t-(3pi)/6))

laplace transform

sin (6 (t - \frac{3 π}{6}))

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

Solution steps

L {sin (6 (t - \frac{3 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{3 π}{6}))} = \frac{s sin ( - 3 π ) + 6 cos ( - 3 π )}{s ^{2} + 6 ^{2}}

= \frac{s sin ( - 3 π ) + 6 cos ( - 3 π )}{s ^{2} + 6 ^{2}}

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

\frac{d}{d x} (x (e^{- x}))

\frac{\partial}{\partial x} (\frac{x y}{e ^{x^{2} + y^{2}}})

ln (arctan (2 x^{3}))

\int \frac{3}{x} + 2 e^{x} d x

\frac{d}{d x} (3 x - x^{2})

What is laplacetransform sin(6(t-(3pi)/6)) ?
The answer to laplacetransform sin(6(t-(3pi)/6)) is -6/(s^2+36)