What is laplacetransform cos(t-(2pi)/3) ?

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

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laplacetransform cos(t-(2pi)/3)

laplace transform

cos (t - \frac{2 π}{3})

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

Solution steps

L {cos (t - \frac{2 π}{3})}

Use Laplace Transform table:

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

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

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

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

x \to 0 lim (\frac{7 ^{x} - 4 ^{x}}{x})

\int \frac{x - 3}{8 x - x ^{2}} d x

\int \frac{2}{4 x ^{2} + 1} d x

\int \frac{1}{1 + x ^{3}} d x

(1, \frac{13}{2}), (6, - 4)

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