Question

sketch the graph in the format of the graph in the picture. only plot the first stated period when plotting. From where it's shifted start begins to the end of that period and nothing else.

Answer 1

Given:

The function is given

`y=2sin(x+(\pi)/(4))+2`

Required:

Find the amplitude and graph the function.

Step-by-step explanation:

compare the equation with the equation

`y=asin(bx+c)+d`

Where a = amplitude

period =

`(2\pi)/(b)`

Phase shift =

`-(c)/(b)`

Vertical shife = d

Compare the given equation with the standard equation we get

a = 2, b = 1,

`c=(\pi)/(4)`

d = 2

Period

`\begin{gathered} =(2\pi)/(b) \\ =(2\pi)/(1) \\ =2\pi \end{gathered}`

Phase shift

`\begin{gathered} =-(c)/(b) \\ =-((\pi)/(4))/(1) \\ c=-(\pi)/(4) \end{gathered}`

Vertical shift d = 2