Trigonometry absolute value

Question

Does absolute value for $\csc(x)$ and for $\operatorname{sec}(x)$ exists in graphs?

$y=|\csc(x)|$ and $y=|\operatorname{sec}(x)|$?

Answer 1

Yes of course you may graph and evaluate $ y=\lvert\csc(x)\rvert$ and $ y=\lvert\sec(x)\rvert$.

You will see many vertical asymptotes at the points were the function is not defined due to dividing by zero.

These vertical asymptotes for $ y=\lvert\csc(x)\rvert$ are at multiples of $\pi$ where $y=\sin(x)$ has its zeros.

Similarly for $y=\lvert\sec(x)\rvert$ you have vertical asymptotes where $y=\cos(x)$ has its zeros.