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

The answer to laplacetransform sin(4t+pi/3) is (sqrt(3)s+4)/(2(s^2+16))

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laplacetransform sin(4t+pi/3)

laplace transform

sin (4 t + \frac{π}{3})

\frac{3 s + 4}{2 ( s ^{2} + 16 )}

Solution steps

L {sin (4 t + \frac{π}{3})}

Use Laplace Transform table:

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

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

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

= \frac{3 s + 4}{2 ( s ^{2} + 16 )}

f (x) = (x^{4} - 2 x)^{5}

\int \frac{1}{3 x ^{2} - 12 x + 15} d x

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

\int \frac{y + 4}{y ^{3} + 2 y ^{2} + 2 y} d y

\frac{d}{d x} (5 x^{3} y)

What is laplacetransform sin(4t+pi/3) ?
The answer to laplacetransform sin(4t+pi/3) is (sqrt(3)s+4)/(2(s^2+16))