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 htt

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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: