What is laplacetransform cos(25pit+pi/2) ?

The answer to laplacetransform cos(25pit+pi/2) is -(25pi)/(s^2+625pi^2)

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laplacetransform cos(25pit+pi/2)

laplace transform

cos (25 π t + \frac{π}{2})

- \frac{25 π}{s ^{2} + 625 π ^{2}}

Solution steps

L {cos (25 π t + \frac{π}{2})}

Use Laplace Transform table:

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

L {cos (25 π t + \frac{π}{2})} = \frac{s cos ( \frac{π}{2} ) - 25 π sin ( \frac{π}{2} )}{s ^{2} + ( 25 π ) ^{2}}

= \frac{s cos ( \frac{π}{2} ) - 25 π sin ( \frac{π}{2} )}{s ^{2} + ( 25 π ) ^{2}}

= - \frac{25 π}{s ^{2} + 625 π ^{2}}

\frac{d y}{d x} = x y - y

\frac{d}{d y} (\frac{x + y}{x y})

y = sin^{4} (x)

\int_{0}^{2} π (2 x)^{2} d x

x \to - 3 lim (8 + x)

What is laplacetransform cos(25pit+pi/2) ?
The answer to laplacetransform cos(25pit+pi/2) is -(25pi)/(s^2+625pi^2)