A3. Which of the following statements is not true for the function $f$ defined by $f(x)=\frac{1}{2}-\frac{1}{2} \cos x$?
(A) The range of the function $f$ is $[0,1]$.
(B) The fundamental period of the function $f$ is $2 \pi$.
(C) The function $f$ is even.
(D) The zeros of the function $f$ are $x=k \pi, k \in \mathbb{Z}$.
(E) The function $f$ achieves its maximum value for $x=\pi+2 k \pi, k \in \mathbb{Z}$.
A3. The zeros of the function $f$ are the solutions of the equation $\frac{1}{2}-\frac{1}{2} \cos x=0$, thus $x=2 k \pi, k \in \mathbb{Z}$, and not $x=k \pi, k \in \mathbb{Z}$.