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

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

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laplacetransform 3sin(5t+45)

laplace transform

3 sin (5 t + 4 5^{\circ})

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

Solution steps

L {3 sin (5 t + 4 5^{\circ})}

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 + 4 5^{\circ})}

L {sin (5 t + 4 5^{\circ})} : \frac{s + 5}{2 ( s ^{2} + 25 )}

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

Refine

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

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

x^{2} - 2 y^{2} + 2 x y y^{^{'}} = 0

\frac{d}{d x} (\frac{1}{4 - x})

\int \frac{1}{3 x - 7} d x

e^{(3 t)}

\frac{d y}{d x} = \frac{2 x + sec ^{2} ( x )}{2 y}, y (0) = - 3

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