what is the period of the graph of y=2sin3A?

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embizze eNotes educator| Certified Educator

What is the period of `y=2sin3A`

(1) Given `y=Asin(B(x-h))+k` the following are the transformations of y=sin(x):

A: a vertical stretch/compression. If A<0 there is a reflection about the x axis. A gives the amplitude.

B: a horizontal stretch/compression. If B<0 there is a reflection across the y-axis. The period is `p=(2pi)/B` .

h: a horizontal translation

k: a vertical translation

(2) Given `y=2sin3A` the period p will be `p=(2pi)/3`

Note that the amplitude will be 2.

(3)The graph of y=sin(x) is in black; the graph of y=2sin(x) is in red; the graph of y=2sin(3x) is in green:

See that there are 3 complete periods from 0 to `2pi~~6.28`