Answer
The function is even.
Zeros: $x=πk$ where k is an integer
Work Step by Step
To check whether a function f is even, odd, or neither, evaluate $f(−x)$. If $f(−x)=f(x)$ then the function is even. If $f(−x)=−f(x)$ then the function is odd. Otherwise the function is neither:
$f(x)=\sin^2 x$
$f(−x)=\sin^2 (-x)$
$f(−x)=(-\sin x)^2$
$f(-x)=\sin^2 x$
$f(−x)=f(x)$
Therefore the function is even.
The zeros of the function occur whenever $\sin x=0$
So the zeros are $x=πk$ where k is an integer
