What is laplacetransform sin(6(t-pi/2)) ?

The answer to laplacetransform sin(6(t-pi/2)) is -6/(s^2+36)

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laplacetransform sin(6(t-pi/2))

laplace transform

sin (6 (t - \frac{π}{2}))

- \frac{6}{s ^{2} + 36}

Solution steps

L {sin (6 (t - \frac{π}{2}))}

Use Laplace Transform table:

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

L {sin (6 (t - \frac{π}{2}))} = \frac{s sin ( - 3 π ) + 6 cos ( - 3 π )}{s ^{2} + 6 ^{2}}

= \frac{s sin ( - 3 π ) + 6 cos ( - 3 π )}{s ^{2} + 6 ^{2}}

= - \frac{6}{s ^{2} + 36}

\int (3 x + 5)^{2} (\frac{7 x - 4}{x ^{2}}) d x

x \to + 0 lim (- \frac{7}{1 - 7 x})

f (x) = 7 x - 3

\frac{d y}{d x}, 5 x^{2} + 3 x y - y^{2} = 2

\frac{d}{d x} (x^{2 c o s (x)})

What is laplacetransform sin(6(t-pi/2)) ?
The answer to laplacetransform sin(6(t-pi/2)) is -6/(s^2+36)