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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.

Sketch The Graph In The Format Of The Graph In The Picture Only Plot The First Stated Period When Plotting From Where Its Shifted Start Begins To The End Of Tha class=
Sketch The Graph In The Format Of The Graph In The Picture Only Plot The First Stated Period When Plotting From Where Its Shifted Start Begins To The End Of Tha class=

Sagot :

Given:

The function is given

[tex]y=2sin(x+\frac{\pi}{4})+2[/tex]

Required:

Find the amplitude and graph the function.

Explanation:

compare the equation with the equation

[tex]y=asin(bx+c)+d[/tex]

Where a = amplitude

period =

[tex]\frac{2\pi}{b}[/tex]

Phase shift =

[tex]-\frac{c}{b}[/tex]

Vertical shife = d

Compare the given equation with the standard equation we get

a = 2, b = 1,

[tex]c=\frac{\pi}{4}[/tex]

d = 2

Period

[tex]\begin{gathered} =\frac{2\pi}{b} \\ =\frac{2\pi}{1} \\ =2\pi \end{gathered}[/tex]

Phase shift

[tex]\begin{gathered} =-\frac{c}{b} \\ =-\frac{\frac{\pi}{4}}{1} \\ c=-\frac{\pi}{4} \end{gathered}[/tex]

Vertical shift d = 2

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