Answer:
[tex]y=acsc(bx-c)+d\\y=csc(\frac{1}{2}x)+2\\P=\frac{2\pi}{b}\Rightarrow P=\frac{2\pi}{\frac{1}{2}} \Rightarrow P = 2\pi*2 \Rightarrow P=4\pi\\d=2[/tex]
Step-by-step explanation:
The trigonometric functions have some features like amplitude, period, phase shift, and vertical shift.
Retrieving the original cosecant graph and copying and attaching it below we have this function:
[tex]y=cosec(\frac{1}{2})x+2[/tex]
1) Period
Since the period of a basic secant and basic sine function [tex]2\pi[/tex]
[tex]y=acsc(bx-c)+d\\y=csc(\frac{1}{2}x)+2\\P=\frac{2\pi}{b}\Rightarrow P=\frac{2\pi}{\frac{1}{2}} \Rightarrow P = 2\pi*2 \Rightarrow P=4\pi[/tex]
2) Vertical Shift
This value affects the graph by displacing it from x-axis.
The Vertical Shift does not need calculation for it is given by the parameter "d"
[tex]y=acsc(bx-c)+d\\y=csc(\frac{1}{2}x)+2\\ d=2 \: (Vertical\:Shift)[/tex]
Answer:
He is right is D
Step-by-step explanation:
