Answer:
Phase shift = [tex]\frac{3\pi }{5}[/tex]
Vertical shift = [tex]0[/tex]
Step-by-step explanation:
Shift Definition
[tex]\text{For\:}f\left(x\right)=A\cdot g\left(Bx-C\right)+D\text{,\:where\:}g\left(x\right)\text{\:is\:one\:of\:the\:basic\:trig\:functions,\:}[/tex] [tex]\frac{C}{B}\text{\:is\:phase\:shift}[/tex], [tex]D\text{\:is\:vertical\:shift}[/tex]
Here we have
[tex]\left(x\right)=4\csc \left(\frac{5\theta-3\pi }{4}\right)[/tex]
which can be written in the form [tex]g\left(Bx-C\right)=\csc \left(\frac{5\theta-3\pi }{4}\right)[/tex]
So comparing the two we get [tex]B=\frac{5}{4}, C=\frac{3\pi }{4},\:D=0[/tex]
Phase shift = [tex]\frac{C}{B} = \frac{\frac{3\pi }{4}}{\frac{5}{4}}[/tex] [tex]= \frac{3\pi }{5}[/tex]
Vertical shift [tex]D = 0[/tex]