Determine Amplitude/period/phase shift /graph function. over 1 period.
Indicate xintercepts and coordinates of Hi/low points on graph.
y = cos (2x - pi/3) +1
y = A ( Bx - C )
so Amplitude is 1
Period: 2pi/B--> 2pi/2 = Pi
Okay is my phase shift right?
Phaseshift = C/B
pi
----
3
--------------- = pi/6?
2

- lilsis76

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- anonymous

looks good to me
i never remember the formula, so i set \(2x-\frac{\pi}{3}=0\) and solve for \(x\)

- anonymous

this also help me remember whether the graph has moved left or right. in this case you get \(x=\frac{\pi}{6}\) so it is shifted to the right

- lilsis76

oh!, okay so since it was positive it goes right, right?
I thought if if was negative it goes right?? i am still confused on how they shift.

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## More answers

- lilsis76

|dw:1349892894075:dw|

- anonymous

think of it this way
for regular old cosine, you know \(\cos(0)=1\)
now you solve \(2x-\frac{\pi}{3}=0\) and you see \(x=\frac{\pi}{6}\) which means instead of \((0,1)\) on the graph, you have \((\frac{\pi}{6},1)\) on the graph, so it is shifted right

- anonymous

hold on, i did not say what you wrote
set it equal to zero
\[2x-\frac{\pi}{3}=0\]
\[2x=\frac{\pi}{3}\]
\[x=\frac{\pi}{6}\]

- anonymous

i meant set \[2x-\frac{\pi}{3}=0\] not
\[2x-\frac{x}{3}=0\]

- lilsis76

haha okay, i thought = to zero

- anonymous

whew

- lilsis76

haha sorry about that

- lilsis76

okay so to figure the points, i start at pi/6 and move right by pi/6?

- anonymous

lets go slow because i do not want to confuse you

- anonymous

you know \(\cos(0)=1\) right?

- lilsis76

okay then. well then what i know know is
Amp = 1
period 2pi/b--> 2pi/3
phase shift---> 2x-pi/3=0--> 2x=pi/3 divide both by 2--> = pi/6 Goes Right
And yes Cos(0)=1 means at the point zero it goes up to 1 which is the highest point

- anonymous

right, so in this case you have to make \(x=\frac{\pi}{6}\) in order to get \(2x-\frac{\pi}{3}=0\) so for your graph, instead of \((0,1)\) you have \((\frac{\pi}{6},1)\) on the graph

- anonymous

all you wrote is correct, here is a nice picture
http://www.wolframalpha.com/input/?i=+y+%3D+cos+%282x+-+pi%2F3%29+%2B1

- lilsis76

OH! i forgot i have to move it up 1

- lilsis76

okay so then i have it like this:
|dw:1349893756732:dw|

- lilsis76

then i move up 1

- lilsis76

|dw:1349893880189:dw|

- lilsis76

@satellite73 Like this?
so amplitude is 1
period is Pi
Phase Shift is pi/6
I graphed the function
the x intercepts: there are not any.
the lowest point is (pi/2,0), and the highest point is (pi/6,2)

- lilsis76

|dw:1349894136637:dw|

- lilsis76

@swissgirl
@marcoduuuh
checked the answers in the back of my book. How did they come up with the x intercept of 2pi/3?
the hight point i got is (pi/6,2) but how do i get (7pi/6, 2)?
the low point of (2pi/3, 0 ) ?

- phi

this curve just touches the x-axis when y=0
cos (2x - pi/3) +1 = 0
cos(2x- pi/3)= -1
arc cos both sides
2x - pi/3 = pi
2x= pi+pi/3 = 4/3 pi
x= 2/3 pi

- lilsis76

how did you do that?

- phi

you know the period is pi, so every time you increase x by pi you will get the same value as x

- lilsis76

sorry, im new to precalculus. all this is super new to me

- phi

the hight point i got is (pi/6,2) but how do i get (7pi/6, 2)?
pi/6 + pi = pi/6 + 6pi/6 = 7pi/6

- phi

how did you do that?
are you asking how to get the lowest point at x= 2/3 pi ?

- lilsis76

oh....okay, now is that going to be the same step for getting the HIghs on all problems like that? you get the Period and add it too the phase shift?
Yes and I cant get the lowest point either, i end up getting pi/2, 0

- phi

Let's look at
How did they come up with the x intercept of 2pi/3?
First, you know x-intercept means the x value where the curve touches or crosses the x-axis?

- lilsis76

yes how did they come up with 2pi/3, because i got...
pi/6 pi/3 pi/2 and wait i guess i got the 2pi/3. but
okay i know and see my question.
how did they get 2pi/3 an point 0, because when i graphed it by hand it shows that 2pi/3 is at 1

- lilsis76

|dw:1349897328597:dw|

- lilsis76

this is the graph i got, but i got pi/2 as my lowest.
did i do something wrong?

- phi

type
y = cos (2x - pi/3) +1
in the google search window, it should graph it

- lilsis76

okay im lookin at the graph

- lilsis76

so how do i figure the lowest with that graph?

- phi

You see the curve just touches the x-axis. This happens when y=0
we start with
y = cos (2x - pi/3) +1
cos (2x - pi/3) +1 = 0 (look for where the curve crosses or touches the x-axis)
use algebra to solve for x:
write -1 on both sides of the =
cos(2x -pi/3) +1 -1 = 0-1 simplify to get
cos(2x-pi/3) = -1

- lilsis76

cos(2x-pi/3) = -1 okay i get this like u did

- phi

cos(2x-pi/3) = -1
take the inverse cosine of both sides
2x -pi/3 = acos(-1)
type in google
acos(-1)=
you get pi radians (3.14159....) or 180 degrees.
you now have
2x -pi/3 = pi
can you finish?

- lilsis76

i end up getting 2pi/3.
and that graph on google is confusing me with different numbers

- phi

The graph is show the curve with x in radians.
the region from x=0 to 2pi (6.283...) is the region your question is asking about.
you see 2 peaks in this interval. Decimals make it hard to match these spots with x= pi/6 and x= 7pi/6
but using a calculator or google we see x= 0.523... and x=3.665...

- phi

*The graph shows the curve with x in radians.

- lilsis76

oh....okay, i understand that now, thank you.
for your help. Imma close this question and fix my homework. Ill be back later. so thank you

- phi

OK. For graphing, I would pick a few x values and use a calculator to find the corresponding y value. Then plot that point. After a few points you can sketch in the curve.

- lilsis76

okay, i would have to try that, I probably wont beable to do that on a quiz tomorrow. she is not allowing calculators. but if i know the steps i know i can do the question or problem

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