What is laplacetransform 3sin(5t+45) ?

The answer to laplacetransform 3sin(5t+45) is (3(sin(45)s+5cos(45)))/(s^2+25)

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laplacetransform 3sin(5t+45)

laplace transform

3 sin (5 t + 45)

\frac{3 ( sin ( 45 ) s + 5 cos ( 45 ) )}{s ^{2} + 25}

Solution steps

L {3 sin (5 t + 45)}

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 (5 t + 45)}

L {sin (5 t + 45)} : \frac{sin ( 45 ) s + 5 cos ( 45 )}{s ^{2} + 25}

= 3 \cdot \frac{sin ( 45 ) s + 5 cos ( 45 )}{s ^{2} + 25}

Refine

3 \frac{sin ( 45 ) s + 5 cos ( 45 )}{s ^{2} + 25} : \frac{3 ( sin ( 45 ) s + 5 cos ( 45 ) )}{s ^{2} + 25}

= \frac{3 ( sin ( 45 ) s + 5 cos ( 45 ) )}{s ^{2} + 25}

\int \frac{( x ^{7} + 3 x ^{5} - 2 x ^{3} - 4 )}{x ^{3}} d x

\frac{\partial}{\partial y} (1000 - 4 x y + x y^{2})

\frac{\partial}{\partial x} (e^{- 3 t} cos (π x))

\int_{0}^{\frac{5}{7}} 5 x - 7 x^{2} d x

x \to 0 + lim (x^{8 x})

What is laplacetransform 3sin(5t+45) ?
The answer to laplacetransform 3sin(5t+45) is (3(sin(45)s+5cos(45)))/(s^2+25)