#color(red)(bar(ul(|color(white)(2/2)color(black)(y=asin(bx+c)+d)color(white)(2/2)|)))#

#"where amplitude "=|a|," duration "=(2pi)/b#

#"phase shift "=-c/b" and also vertical change "=d#

#"here "a=2,b=1,c=d=0#

#rArr"amplitude "=|2|=2," period "=2pi# the amplitude the #y = sin x# is #1#.

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#(sin x)# is multiplied by #2#, i.e. After ~ the function #sin x# has actually been applied, the result is multiply by #2#.

the result of #sin x# because that the graph #y = sinx# is #y# in ~ any allude on the graph.

the an outcome of #2 sin x# because that the graph #y = sin x# would certainly be #2y# at any allude on the graph.

since #y# is the upright axis, changing the coefficient that #(sin x)# changes the vertical height of the graph.

the amplitude is the value of the distance between the #x#-axis and also the greatest or lowest point on the graph.

for #y = (1) sin x#, the amplitude is #1#.

for #y = 2 sin x#, the amplitude is #2#.

the duration of a graph is how frequently the graph repeats itself.

the graph that #y = sin x# will certainly repeat its sample every #360^
#. #sin 0^
= sin 360^
= 1#, #sin 270^
= sin 630^
= -1#, etc. (the graph shown is #y = sin x# where #0^
)

if the worth that the duty #sin# is being applied to changes, the graph will readjust along the #x#-axis.

e.g. If the worth is changed to #y = sin 2x#, #y# will be #sin 90^
# at #x = 45^
#, and #sin 360^
# in ~ #x = 180^
#.

the range of the worths that #y# can take will remain the same, however they will be at various points the #x#.

if the coefficient that #x# is increased, the highest and also lowest points on the graph will certainly seem closer together.

however, the duty in concern does not the coefficient of #(x)# - only the coefficient the #(sin x)#.

the range of worths that #y# have the right to take is doubled, yet #x# will repeat itself at the very same points.

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the amplitude is #2#, and also the period is #360^
#. 