Question 820903
Question 820903
<pre>
y=-3sin (x-pi/4)+1 

First we draw the graph of 

y = sin(x)

{{{drawing(400,8000/17,-.5,8,-5,5, graph(400,8000/17,-.5,8,-5,5,

sin(x)*sqrt(sin(15x))/sqrt(sin(15x))*(sqrt(2pi-x)/sqrt(2pi-x))*(sqrt(x)/sqrt(x))


),locate(1.5,0,pi/2),locate(3,.4,pi),locate(4.5,.9,3pi/2),
green(line(pi/2,0,pi/2,1),line(3pi/2,0,3pi/2,-1)),locate(6.1,0,2pi)


)}}}

Then we draw the graph of y = 3sin(x) which stretches it three times as high
and low

{{{drawing(400,8000/17,-.5,8,-5,5, graph(400,8000/17,-.5,8,-5,5,

3sin(x)*sqrt(sin(20x))/sqrt(sin(20x))*(sqrt(2pi-x)/sqrt(2pi-x))*(sqrt(x)/sqrt(x))


),locate(1.5,0,pi/2),locate(3,.4,pi),locate(4.5,.9,3pi/2),
green(line(pi/2,0,pi/2,3),line(3pi/2,0,3pi/2,-3)),locate(6.1,0,2pi)


)}}}

Then we draw the graph of y = -3sin(x) which reflects the graph in the y axis

{{{drawing(400,8000/17,-.5,8,-5,5, graph(400,8000/17,-.5,8,-5,5,

-3sin(x)*sqrt(sin(20x))/sqrt(sin(20x))*(sqrt(2pi-x)/sqrt(2pi-x))*(sqrt(x)/sqrt(x))


),locate(1.5,.9,pi/2),locate(3,.4,pi),locate(4.5,0,3pi/2),
green(line(pi/2,0,pi/2,-3),line(3pi/2,0,3pi/2,3)),locate(6.1,0,2pi) )}}}

Then we draw the graph of y = -3sin(x-pi/4) which shifts it right by pi/4 units.

But to do that we take each of the 5 main points, 0,{{{pi/2}}},{{{pi}}},{{{3pi/2}}} and {{{2pi}}} and add {{{pi/4}}} to each"

{{{0+pi/4}}} = {{{pi/4}}}
{{{pi/2+pi/4}}} = {{{2pi/4+pi/4}}} = {{{3pi/4}}}
{{{pi+pi/4}}} = {{{4pi/4+pi/4}}} = {{{5pi/4}}}
{{{3pi/2+pi/4}}} = {{{6pi/4+pi/4}}} = {{{7pi/4}}}
{{{2pi+pi/4}}} = {{{8pi/4+pi/4}}} = {{{9pi/4}}}

{{{drawing(400,8000/17,-.5,8,-5,5, graph(400,8000/17,-.5,8,-5,5,

-3sin(x-pi/4)*sqrt(sin(25x))/sqrt(sin(25x))*(sqrt(9pi/4-x)/sqrt(9pi/4-x))*(sqrt(x-pi/4)/sqrt(x-pi/4))),
locate(pi/4,.9,pi/4)

,locate(1.5+pi/4,.9,3pi/4),locate(3+pi/4,.4,5pi/4),locate(4.5+pi/4,0,7pi/4),
green(line(pi/2+pi/4,0,pi/2+pi/4,-3),line(3pi/2+pi/4,0,3pi/2+pi/4,3)),locate(6.1+pi/4,0,9pi/4) )}}}


Then we draw the graph of y = -3sin(x-pi/4)+1 which shifts the graph up 1 unit.

{{{drawing(400,8000/17,-.5,8,-5,5, graph(400,8000/17,-.5,8,-5,5,

(-3sin(x-pi/4)+1)*sqrt(sin(25x))/sqrt(sin(25x))*(sqrt(9pi/4-x)/sqrt(9pi/4-x))*(sqrt(x-pi/4)/sqrt(x-pi/4)),1*(sqrt(9pi/4-x)/sqrt(9pi/4-x))),
locate(pi/4,.9,pi/4),

locate(1.5+pi/4,.9,3pi/4),locate(3+pi/4,.4,5pi/4),locate(4.5+pi/4,0,7pi/4),
green(line(pi/2+pi/4,1,pi/2+pi/4,-2),line(3pi/2+pi/4,1,3pi/2+pi/4,4)),locate(6.1+pi/4,0,9pi/4) )}}}

Edwin</pre>