Question

What are the period and vertical shift of the cosecant function below?

Answer 1

Answer:

$y=acsc(bx-c)+d\\y=csc(\frac{1}{2}x)+2\\P=\frac{2\pi}{b}\Rightarrow P=\frac{2\pi}{\frac{1}{2}} \Rightarrow P = 2\pi*2 \Rightarrow P=4\pi\\d=2$

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:

$y=cosec(\frac{1}{2})x+2$

1) Period

Since the period of a basic secant and basic sine function $2\pi$

$y=acsc(bx-c)+d\\y=csc(\frac{1}{2}x)+2\\P=\frac{2\pi}{b}\Rightarrow P=\frac{2\pi}{\frac{1}{2}} \Rightarrow P = 2\pi*2 \Rightarrow P=4\pi$

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"

$y=acsc(bx-c)+d\\y=csc(\frac{1}{2}x)+2\\ d=2 \: (Vertical\:Shift)$

Answer 2

Answer:

He is right is D

Step-by-step explanation: