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