How to plot the graph of #f(x)=2 sin 4x#?

1 Answer
Alan P.
Jul 22, 2015

Draw a standard #sin# curve but "squeeze" the vertical so the period is reduced from #2pi# to #pi/2# and stretch the horizontal so the amplitude is increased from #[-1,1]# to #[-2, 2]#

Explanation:

#sin(theta)# has a period of #2pi#
replacing #theta# by #4x# means that #4x# must have the same period
and therefore each #x# of the #4x# can only take up #(2pi)/4 = pi/2# period length.

#sin(theta)# has an amplitude of #[-1,+1]#
#rarr# for any angle #4x#, #sin(4x)# must be a value #s epsilon [-1,+1]#
and
#rarr 2sin(4x)# must be #2s# giving it a range of #[-2,+2]#

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