What is laplacetransform sin(100t+30) ?

The answer to laplacetransform sin(100t+30) is (sin(30)s+100cos(30))/(s^2+10000)

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laplacetransform sin(100t+30)

laplace transform

sin (100 t + 30)

\frac{sin ( 30 ) s + 100 cos ( 30 )}{s ^{2} + 10000}

Solution steps

L {sin (100 t + 30)}

Use Laplace Transform table:

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

L {sin (100 t + 30)} = \frac{s sin ( 30 ) + 100 cos ( 30 )}{s ^{2} + 10 0 ^{2}}

= \frac{s sin ( 30 ) + 100 cos ( 30 )}{s ^{2} + 10 0 ^{2}}

= \frac{sin ( 30 ) s + 100 cos ( 30 )}{s ^{2} + 10000}

x \to - \infty lim (\frac{8 x ^{2} + 7 x ^{\frac{1}{3}}}{16 x ^{4} + 6})

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

\int \frac{1}{2 x - x ^{2}} d x

d er i v a t i v e f (x) = - 3 sin (3 x)

\int \frac{1}{7 x ^{2} - 8} d x

What is laplacetransform sin(100t+30) ?
The answer to laplacetransform sin(100t+30) is (sin(30)s+100cos(30))/(s^2+10000)