What is laplacetransform 3sin(3t+2) ?

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

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laplacetransform 3sin(3t+2)

laplace transform

3 sin (3 t + 2)

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

Solution steps

L {3 sin (3 t + 2)}

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)}

= 3 L {sin (3 t + 2)}

L {sin (3 t + 2)} : \frac{sin ( 2 ) s + 3 cos ( 2 )}{s ^{2} + 9}

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

Refine

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

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

\int 4 x^{3} e^{2 x^{4}} d x

\frac{d}{d x} ((\frac{x ^{2}}{6 - x})^{5})

\int_{0}^{1} x^{4} - 2 x^{3} + x^{2} d x

\frac{\partial}{\partial x} (9 - 2 x^{2} + 3 y^{2})

\frac{\partial}{\partial x} (cos (2 x + 5 y) \cdot 5)

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