What is laplacetransform sin(5t-pi/3) ?

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

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laplacetransform sin(5t-pi/3)

laplace transform

sin (5 t - \frac{π}{3})

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

Solution steps

L {sin (5 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 (5 t - \frac{π}{3})} = \frac{s sin ( - \frac{π}{3} ) + 5 cos ( - \frac{π}{3} )}{s ^{2} + 5 ^{2}}

= \frac{s sin ( - \frac{π}{3} ) + 5 cos ( - \frac{π}{3} )}{s ^{2} + 5 ^{2}}

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

x \to \infty lim ((\frac{x}{x + 1})^{2 x})

\frac{d}{d x} (a x^{3} + b x^{2})

\frac{d}{d x} (\frac{- 3}{x + 1})

n = 1 \sum \infty \frac{n ^{8}}{n !}

\frac{d}{d x} (x^{3} - x^{2} - 6 x)

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