SOLUTION: Please help!
The graph of one complete period of a sine and cosine curve is given.?
please explain how to fill out these graphs thank you
http://i.imgur.com/rCXQUym.png
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Question 921246: Please help!
The graph of one complete period of a sine and cosine curve is given.?
please explain how to fill out these graphs thank you
http://i.imgur.com/rCXQUym.png
http://i.imgur.com/X1cZq8F.png
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your first picture is shown below:
the interval goes from 0 to 4p/4 which is the same as from 0 to pi.
the period is therefore equal to pi.
the frequency is equal to 2pi / pi = 2
there is no phase shift because cosine = 1 at 0 radians which is the value shown on the graph.
the equation in the form of y = a * cos (k(x-b)) becomes:
y = 6 * cos(2 * x)
i graphed it to confirm.
that graph is shown below:
you can see the equation on the top left.
the graph matches your picture so it looks good.
your second picture is shown below:
the amplitude is 6.
the interval goes from -3/4 to 1/4.
the period is therefore equal to 1.
the frequency is equal to 2pi / 1 = 2pi.
the sine wave should be 0 when x = 0.
this sine wave appears to be shifted to the right by 1/4 of the period.
the phase shift is therefore equal to 1/4.
the equation in the form of y = a * sin (k * (x-b)) becomes:
y = 6 * sin(2pi * (x-1/4))
the graph of that equation is shown below:
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