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

The answer to laplacetransform sin(t+pi/3) is (sqrt(3)s+1)/(2(s^2+1))

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laplacetransform sin(t+pi/3)

laplace transform

sin (t + \frac{π}{3})

\frac{3 s + 1}{2 ( s ^{2} + 1 )}

Solution steps

L {sin (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 (t + \frac{π}{3})} = \frac{s sin ( \frac{π}{3} ) + 1 \cdot cos ( \frac{π}{3} )}{s ^{2} + 1 ^{2}}

= \frac{s sin ( \frac{π}{3} ) + 1 \cdot cos ( \frac{π}{3} )}{s ^{2} + 1 ^{2}}

= \frac{3 s + 1}{2 ( s ^{2} + 1 )}

f (x) = - 3

\int_{- 2}^{1} x d x

\frac{d y}{d x} = e^{2 x + 5 y}

\frac{d}{d x} (\frac{x ^{2} - 9 x + 7}{x ^{2} + 9})

10 tan^{2} (6 x)

What is laplacetransform sin(t+pi/3) ?
The answer to laplacetransform sin(t+pi/3) is (sqrt(3)s+1)/(2(s^2+1))