laplacetransform sin(t+pi/4)

解答

拉普拉斯变换

sin (t + \frac{π}{4})

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

求解步骤

L {sin (t + \frac{π}{4})}

使用拉普拉斯变换表:

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

L {sin (t + \frac{π}{4})} = \frac{s sin ( \frac{π}{4} ) + 1 \cdot cos ( \frac{π}{4} )}{s ^{2} + 1 ^{2}}

= \frac{s sin ( \frac{π}{4} ) + 1 \cdot cos ( \frac{π}{4} )}{s ^{2} + 1 ^{2}}

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

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