Question 910128
{{{y = sin(x) + 5}}} is the same as {{{y = 1*sin(1*x-0) + 5}}}


Compare {{{y = 1*sin(1*x-0) + 5}}} to the general form {{{y = A*sin(B*x-C) + D}}}


We see that


A = 1
B = 1
C = 0
D = 5


So...


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Amplitude: |A| = |1| = 1


The amplitude is 1


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Period: 


T = period


T = 2pi/B


T = 2pi/1


T = 2pi


The period is 2pi


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Phase Shift:


C is the phase shift. Since C = 0, the phase shift is 0. The parent function y = sin(x) has not been moved left or right.


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Midline:


The midline is the center horizontal line that goes through the sine or cosine function.


Since D = 5, the midline is the horizontal line y = 5. Essentially, this means that the y = sin(x) graph has been shifted 5 units up.


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Graph of {{{y = sin(x) + 5}}} in <font color="red">red</font>. Midline is the <font color="blue">blue</font> dashed horizontal line that cuts through the center of the sine curve.


<img src = "http://i150.photobucket.com/albums/s91/jim_thompson5910/10-6-20145-56-20PM_zpsfd7ae48f.png">