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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
 one year ago
 one year ago
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
 one year ago
 one year ago

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satellite73Best ResponseYou've already chosen the best response.0
looks good to me i never remember the formula, so i set \(2x\frac{\pi}{3}=0\) and solve for \(x\)
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
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
 one year ago

lilsis76Best ResponseYou've already chosen the best response.1
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.
 one year ago

lilsis76Best ResponseYou've already chosen the best response.1
dw:1349892894075:dw
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
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
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
hold on, i did not say what you wrote set it equal to zero \[2x\frac{\pi}{3}=0\] \[2x=\frac{\pi}{3}\] \[x=\frac{\pi}{6}\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
i meant set \[2x\frac{\pi}{3}=0\] not \[2x\frac{x}{3}=0\]
 one year ago

lilsis76Best ResponseYou've already chosen the best response.1
haha okay, i thought = to zero
 one year ago

lilsis76Best ResponseYou've already chosen the best response.1
haha sorry about that
 one year ago

lilsis76Best ResponseYou've already chosen the best response.1
okay so to figure the points, i start at pi/6 and move right by pi/6?
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
lets go slow because i do not want to confuse you
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
you know \(\cos(0)=1\) right?
 one year ago

lilsis76Best ResponseYou've already chosen the best response.1
okay then. well then what i know know is Amp = 1 period 2pi/b> 2pi/3 phase shift> 2xpi/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
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
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
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
all you wrote is correct, here is a nice picture http://www.wolframalpha.com/input/?i=+y+%3D+cos+%282x++pi%2F3%29+%2B1
 one year ago

lilsis76Best ResponseYou've already chosen the best response.1
OH! i forgot i have to move it up 1
 one year ago

lilsis76Best ResponseYou've already chosen the best response.1
okay so then i have it like this: dw:1349893756732:dw
 one year ago

lilsis76Best ResponseYou've already chosen the best response.1
dw:1349893880189:dw
 one year ago

lilsis76Best ResponseYou've already chosen the best response.1
@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)
 one year ago

lilsis76Best ResponseYou've already chosen the best response.1
dw:1349894136637:dw
 one year ago

lilsis76Best ResponseYou've already chosen the best response.1
@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 ) ?
 one year ago

phiBest ResponseYou've already chosen the best response.1
this curve just touches the xaxis 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
 one year ago

phiBest ResponseYou've already chosen the best response.1
you know the period is pi, so every time you increase x by pi you will get the same value as x
 one year ago

lilsis76Best ResponseYou've already chosen the best response.1
sorry, im new to precalculus. all this is super new to me
 one year ago

phiBest ResponseYou've already chosen the best response.1
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
 one year ago

phiBest ResponseYou've already chosen the best response.1
how did you do that? are you asking how to get the lowest point at x= 2/3 pi ?
 one year ago

lilsis76Best ResponseYou've already chosen the best response.1
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
 one year ago

phiBest ResponseYou've already chosen the best response.1
Let's look at How did they come up with the x intercept of 2pi/3? First, you know xintercept means the x value where the curve touches or crosses the xaxis?
 one year ago

lilsis76Best ResponseYou've already chosen the best response.1
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
 one year ago

lilsis76Best ResponseYou've already chosen the best response.1
dw:1349897328597:dw
 one year ago

lilsis76Best ResponseYou've already chosen the best response.1
this is the graph i got, but i got pi/2 as my lowest. did i do something wrong?
 one year ago

phiBest ResponseYou've already chosen the best response.1
type y = cos (2x  pi/3) +1 in the google search window, it should graph it
 one year ago

lilsis76Best ResponseYou've already chosen the best response.1
okay im lookin at the graph
 one year ago

lilsis76Best ResponseYou've already chosen the best response.1
so how do i figure the lowest with that graph?
 one year ago

phiBest ResponseYou've already chosen the best response.1
You see the curve just touches the xaxis. 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 xaxis) use algebra to solve for x: write 1 on both sides of the = cos(2x pi/3) +1 1 = 01 simplify to get cos(2xpi/3) = 1
 one year ago

lilsis76Best ResponseYou've already chosen the best response.1
cos(2xpi/3) = 1 okay i get this like u did
 one year ago

phiBest ResponseYou've already chosen the best response.1
cos(2xpi/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?
 one year ago

lilsis76Best ResponseYou've already chosen the best response.1
i end up getting 2pi/3. and that graph on google is confusing me with different numbers
 one year ago

phiBest ResponseYou've already chosen the best response.1
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...
 one year ago

phiBest ResponseYou've already chosen the best response.1
*The graph shows the curve with x in radians.
 one year ago

lilsis76Best ResponseYou've already chosen the best response.1
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
 one year ago

phiBest ResponseYou've already chosen the best response.1
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.
 one year ago

lilsis76Best ResponseYou've already chosen the best response.1
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
 one year ago
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