Question 841730
<pre>
The basic graph of y = sin(x) has these 5 major points, 

zero,max,zero,min,zero, which are:

(0,0), ({{{pi/2}}},1), {{{pi}}},0), ({{{3pi/2}}},1), ({{{2pi}}},0)

Your graph has the corresponding 5 major points, starting
with the point nearest the origin:

({{{-pi/4}}},0), ({{{pi/4}}},-3), {{{3pi/4}}},0), ({{{5pi/4}}},1), ({{{7pi/4}}},0)

The period is {{{2pi}}} since the last x value of the five is {{{7pi/4}}}, and
the first of the five is {{{-pi/4}}}, so they have difference 

{{{7pi/4-(-pi/4)}}}={{{7pi/4+pi/4}}}={{{8pi/4}}}={{{2pi}}}, 

same as the basic sine graph, {{{2pi-0}}}={{{2pi}}} so there is no horizontal
stretching or shrinking.

Each of the 5 major x-coordinates of your graph is pi/4 less than its
corresponding x-coordinate on the basic sine graph:

{{{0-(-pi/4)}}}={{{pi/2-pi/4}}}={{{pi-3pi/4}}}={{{3pi/2-3pi/4}}}={{{2pi-7pi/4}}}={{{pi/4}}}

So the horizontal shift, commonly called the phase shift, is {{{pi/4}}} units to the 
left.  Therefore the equation of your graph will have (x-{{{-pi/4}}}) or{{{x+pi/4}}} substituted
for x.

Each of the 5 major y-coordinates of the basic sine graph are 0,1,0,-1,0,
whereas the 5 corresponding major y-coordinates of your graph are 0,-3,0,3,0,
They are all multiplied by -3.  The negative sign reflects the graph in the 
x-axis and the 3 stretches it by a factor of 3 vertically.  Therefore the right
side of the equation of your graph will have a factor of -3.  So the equation
of your graph is found by starting with the basic sine graph:

y = sin(x)

Then replace the x by {{{x+pi/4}}} and multiply the right side by -3, and get

y = -3sin{{{(x+pi/4)}}}.

Edwin</pre>