While reflecting a point about the $y$-axis, the magnitude of its $x$-coordinate remains the same but its sign changes. But the $y$-coordinate remains the same. This is because we are taking it to the quadrant beside it. So, we can say that ${\text{R}}_{y}(x,y) = (-x,y)$.
Even functions are functions that satisfy $f(x) = f(-x)$ for all $x.$ Even functions are symmetric about the line $x =0$ (means $y$-axis).
Odd functions are functions that satisfy $f(x) = -f(-x)$ for all $x.$ Odd functions exhibit point symmetry about the origin.
We know that,
- $\sin(-x) = -\sin x$ (odd function)
- $\cos(-x) = \cos x$ (even function)
- $\sec(-x) = \sec x$ (even function)
- $\csc(-x) = -\csc x$ (odd function)
$\therefore$ Clearly the function should be even.
So, the correct answer is $B;C.$