What is the amplitude and period of #y=2sinx#?

Question

Caroline Adams · Accepted Answer

#2,2pi# #"the standard form of the "color(blue)"sine function"# is. #color(red)(bar(ul(|color(white)(2/2)color(black)(y=asin(bx+c)+d)color(white)(2/2)|)))# #"where amplitude "=|a|," period "=(2pi)/b# #"phase shift "=-c/b" and vertical shift "=d# #"here "a=2,b=1,c=d=0# #rArr"amplitude "=|2|=2," period "=2pi#

Quinn Anderson · Answer

amplitude: #2#
period: #360^@#

the amplitude of #y = sin x# is #1#.

#(sin x)# is multiplied by #2#, i.e. after the function #sin x# has been applied, the result is multiplied by #2#.

the result of #sin x# for the graph #y = sinx# is #y# at any point on the graph.

the result of #2 sin x# for the graph #y = sin x# would be #2y# at any point on the graph.

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

the amplitude is the value of the distance between the #x#-axis and the highest 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 period of a graph is how often the graph repeats itself.

the graph of #y = sin x# will repeat its pattern every #360^@#. #sin 0^@ = sin 360^@ = 1#, #sin 270^@ = sin 630^@ = -1#, etc.

James Adkins · Answer

undefined The amplitude of the function $ y = 2\sin(x) $ is $ 2 $, and the period is $ 2\pi $.