How do you find the amplitude and period of #y= 1/4 sin x#?

1 Answer
Alan P.
Jul 22, 2015

The period of #y = 1/4sin(x)# is #2pi#
The amplitude of #y=1/4sin(x)# is #1/4#
#color(white)("XXXX")##color(white)("XXXX")##color(white)("XXXX")#(that is #y epsilon [-1/4, +1/4]#)

Explanation:

The period of #sin(x)# is #2pi#
Multiplying #sin(x)# by a constant only stretches the graph vertically by whatever that constant is; it does not change (for example) the points at which #sin(x)# returns to #0#.

As noted above, multiplying #sin(x)# by a constant stretches it's value by that constant.
Since the range of #sin(x)# is #[-1, +1]#
#color(white)("XXXX")#the range of #1/4sin(x)# is #[-1/4, +1/4]#
#rArr# an amplitude of #1/4#

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