Hallo,
a) y= cos(x-π) -sin(x+π)
Additionstheoreme verwenden:
\( \cos (\alpha-\beta)=\cos \alpha \cdot \cos \beta+\sin \alpha \cdot \sin \beta \)
\( \sin (\alpha+\beta)=\sin \alpha \cdot \cos \beta+\cos \alpha \cdot \sin \beta \)
cos(x-π) = cos(x) cos(π) +sin(x) sin(π) = cos(x)*(-1) +sin(x) *0 = -cos(x)
sin(x+π)=sin(x) *cos(π) +cos(x) sin(π) =sin(x) *(-1) +cos(x) *0= -sin(x)
->= -cos(x) -(-sin(x))= sin(x) -cos(x)
allgemein:
\( f(t)=\frac{a_{0}}{2}+\sum \limits_{k=1}^{\infty}\left(a_{k} \cdot \cos \left(k \omega_{1} t\right)+b_{k} \cdot \sin \left(k \omega_{1} t\right)\right) \)
a= -1
b= 1