What is laplacetransform 3cos(t+pi/3) ?

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

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laplacetransform 3cos(t+pi/3)

laplace transform

3 cos (t + \frac{π}{3})

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

Solution steps

L {3 cos (t + \frac{π}{3})}

Use the constant multiplication property of Laplace Transform:

For function

f (t)

and constant

a : L {a \cdot f (t)} = a \cdot L {f (t)}

= 3 L {cos (t + \frac{π}{3})}

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

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

Refine

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

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

\frac{d}{d x} (cot (7 x))

\int \frac{1}{x ^{2}} - \frac{1}{x ^{3}} d x

x \to 0 lim (\frac{1}{2 x - 1})

\frac{d}{d u} (x^{2} + x y (x, u) (x, u)^{3})

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