26 The function $y=A \sin (\omega x+\varphi$ ) (where $A>0, w>0, x \in \mathbf{R}$ ) is an even function if and only if
A. $\varphi=\frac{2 \pi}{\omega}$
B. $\varphi=-\frac{2 \pi}{\omega}$
C. $\varphi=k \pi(k \in \mathbf{Z})$
D. $\varphi=k \pi+\frac{\pi}{2}(k \in \mathbf{Z})$
26 D. From $A \sin (\omega x+\varphi)=A \sin (-\omega x+\varphi)$, i.e., $\sin (\omega x+\varphi)-\sin (-\omega x+\varphi)=0$, we get $\cos \varphi \sin \omega x=0$, so $\varphi=k \pi+\frac{\pi}{2}(k \in \mathbf{Z})$.