Question 1168728
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Fit each one into the standard form<br>
{{{a*sin(b(x-c))+d}}} or {{{a*cos(b(x-c))+d}}}<br>
In that form...<br>
|a| is the amplitude (that is, the amplitude is always considered positive)
b gives the period; the period is (2pi)/b
c is the horizontal shift
d is the vertical shift<br>
The only work you sometimes need to do is to get the "x" without a coefficient.  For example, if the definition includes "sin(3x-pi)", you need to change it to "sin(3(x-pi/3))".<br>
Also note that the inner parentheses must be in the form (x-c); if the given function shows (x+2), it has to be seen as (x-(-2)), making the horizontal shift -2.<br>
I'll do one similar example; you can do the ones you show in your post.<br>
{{{f(x) = -2cos(3x+pi)-3}}}<br>
Rewrite it in standard form:<br>
{{{f(x) = -2cos(3(x-(-pi/3)))-3}}}<br>
The amplitude is |a| = |-2| = 2
The period is (2pi)/b = (2pi)/3
The horizontal shift is -pi/3
The vertical shift is -3<br>