What is laplacetransform sin(3t+pi/4) ?

The answer to laplacetransform sin(3t+pi/4) is (s+3)/(sqrt(2)(s^2+9))

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laplacetransform sin(3t+pi/4)

laplace transform

sin (3 t + \frac{π}{4})

\frac{s + 3}{2 ( s ^{2} + 9 )}

Solution steps

L {sin (3 t + \frac{π}{4})}

Use Laplace Transform table:

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

L {sin (3 t + \frac{π}{4})} = \frac{s sin ( \frac{π}{4} ) + 3 cos ( \frac{π}{4} )}{s ^{2} + 3 ^{2}}

= \frac{s sin ( \frac{π}{4} ) + 3 cos ( \frac{π}{4} )}{s ^{2} + 3 ^{2}}

= \frac{s + 3}{2 ( s ^{2} + 9 )}

e^{x} - x^{8}

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y = 6 x^{2} - 10 x - 5 x^{- 2}

\frac{\partial}{\partial x} (2 k l ln (\frac{x - n}{n - x}))

What is laplacetransform sin(3t+pi/4) ?
The answer to laplacetransform sin(3t+pi/4) is (s+3)/(sqrt(2)(s^2+9))