laplacetransform cos(t+pi/5)

解

ラプラス変換

cos (t + \frac{π}{5})

\frac{2 ( 5 + 1 ) s - 2 5 - 5}{4 2 ( s ^{2} + 1 )}

解答ステップ

L {cos (t + \frac{π}{5})}

ラプラス変換表を使用する:

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

L {cos (t + \frac{π}{5})} = \frac{s cos ( \frac{π}{5} ) - 1 \cdot sin ( \frac{π}{5} )}{s ^{2} + 1 ^{2}}

= \frac{s cos ( \frac{π}{5} ) - 1 \cdot sin ( \frac{π}{5} )}{s ^{2} + 1 ^{2}}

= \frac{2 ( 5 + 1 ) s - 2 5 - 5}{4 2 ( s ^{2} + 1 )}