Question

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

Answer is D period: 4 pi; vertical shift: 2 units up

Answer 1

He is right is D

Explanation:

Answer 2

`y=acsc(bx-c)+d\\y=csc((1)/(2)x)+2\\P=(2\pi)/(b)\Rightarrow P=(2\pi)/((1)/(2)) \Rightarrow P = 2\pi*2 \Rightarrow P=4\pi\\d=2`

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((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((1)/(2)x)+2\\P=(2\pi)/(b)\Rightarrow P=(2\pi)/((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((1)/(2)x)+2\\ d=2 \: (Vertical\:Shift)`