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