Question 388660
<pre>
For:

f(x) = Asin(Bx + C) + D

Amplitude = |A|
Period = {{{2pi/B}}}
Phase shift = {{{C/B}}}, left if {{{C/B}}} is positive, right if {{{C/B}}} is negative

Vertical shift = D, up if D positive, down if D is negative.

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For:

Graph f(x) = sin (x &#8722; 2&#960;) &#8722; 1

f(x) = 1sin(1x + 2<font face = "symbol">p</font>) - 1

A = 1, B = 1, C = -2<font face = "symbol">p</font>, D = -1



Amplitude = |A| = |1| = 1
Period = {{{2pi/B}}} = {{{2pi/1}}} = {{{2pi}}}
Phase shift = {{{C/B}}} = {{{(-2)/1}}} = -2, right since {{{-2}}} is negative

Vertical shift = D = -1, down since D -1 is negative.

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Graph:  Since the phase shift in absolute value equals the period, the
graph of 

f(x) = sin(x &#8722; 2&#960;) &#8722; 1

is the same as the graph of

f(x) = sin(x) &#8722; 1


{{{drawing(400,160,-5,10,-4,2, green(line(-6,-1,11,-1)),


graph(400,160,-5,10,-4,2,sin(x) - 1))}}}

Edwin</pre>