Answer:
\(\frac{\pi}{3}\)
Step-by-step explanation:
We are asked to find the phase shift of the function \(y=-\text{csc}(3x-\pi)\).
We know that a function of form \(f(x)=a\cdot \text{csc}(bx-c)+d\), where,
\(\text{Period}=\frac{2\pi}{|b|}\),
\(\text{Phase shift}=\frac{c}{b}\),
\(\text{Vertical shift}=d\)
Upon comparing our given function with standard function we can see that \(a=-1\), \(b=3\) and \(c=\pi\).
\(\text{Phase shift}=\frac{\pi}{3}\)
Therefore, the phase shift for our given function is \(\frac{\pi}{3}\).
