1. The graph of the function $y=f(x)$ is translated by the vector $a=$ $\left(\frac{\pi}{4}, 2\right)$, resulting in the graph with the equation $y=$ $\sin \left(x+\frac{\pi}{4}\right)+2$. Therefore, the equation of $y=f(x)$ is
(A) $y=\sin x$
(B) $y=\cos x$
(C) $y=\sin x+2$
(D) $y=\cos x+4$
1. B.
$y=\sin \left[\left(x+\frac{\pi}{4}\right)+\frac{\pi}{4}\right]$, i.e., $y=\cos x$.