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Graph two full periods, highlighting the first period using bold marking and analyze each function.Y = 2 sin (1/2 (x + pi/2) ) + 1

Graph Two Full Periods Highlighting The First Period Using Bold Marking And Analyze Each FunctionY 2 Sin 12 X Pi2 1 class=

Answer :

Given

[tex]y=2\sin(\frac{1}{2}(x+\frac{\pi}{2}))+1[/tex]

Procedure

Period: 4pi

Interval length: In the graph 2 periods 8pi

Phase shift: -pi/2

1st Per. begins: -pi/2

1st Per. ends: 7pi/2

Amplitude: 2

Domain:

(-∞, ∞)

Range:

[-1,3]

y-intercep:

(0,2.414)

x-intercept:

[tex]x=\frac{11\pi}{6}+4\pi n,\frac{19\pi}{6}+4\pi n,\text{ for any integer of n }[/tex]

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