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 2 years 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
 2 years 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

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satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0looks good to me i never remember the formula, so i set \(2x\frac{\pi}{3}=0\) and solve for \(x\)

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0this 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
 2 years ago
Best ResponseYou've already chosen the best response.1oh!, 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.

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0think 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

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0hold on, i did not say what you wrote set it equal to zero \[2x\frac{\pi}{3}=0\] \[2x=\frac{\pi}{3}\] \[x=\frac{\pi}{6}\]

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0i meant set \[2x\frac{\pi}{3}=0\] not \[2x\frac{x}{3}=0\]

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.1haha okay, i thought = to zero

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.1okay so to figure the points, i start at pi/6 and move right by pi/6?

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0lets go slow because i do not want to confuse you

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0you know \(\cos(0)=1\) right?

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.1okay 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

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0right, 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

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0all you wrote is correct, here is a nice picture http://www.wolframalpha.com/input/?i=+y+%3D+cos+%282x++pi%2F3%29+%2B1

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.1OH! i forgot i have to move it up 1

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.1okay so then i have it like this: dw:1349893756732:dw

lilsis76
 2 years ago
Best 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)

lilsis76
 2 years ago
Best 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 ) ?

phi
 2 years ago
Best ResponseYou've already chosen the best response.1this 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

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

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.1sorry, im new to precalculus. all this is super new to me

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

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.1oh....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
 2 years ago
Best ResponseYou've already chosen the best response.1Let'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?

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.1yes 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
 2 years ago
Best ResponseYou've already chosen the best response.1this is the graph i got, but i got pi/2 as my lowest. did i do something wrong?

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

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.1okay im lookin at the graph

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.1so how do i figure the lowest with that graph?

phi
 2 years ago
Best ResponseYou've already chosen the best response.1You 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

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.1cos(2xpi/3) = 1 okay i get this like u did

phi
 2 years ago
Best ResponseYou've already chosen the best response.1cos(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?

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.1i end up getting 2pi/3. and that graph on google is confusing me with different numbers

phi
 2 years ago
Best ResponseYou've already chosen the best response.1The 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
 2 years ago
Best ResponseYou've already chosen the best response.1*The graph shows the curve with x in radians.

lilsis76
 2 years ago
Best ResponseYou've already chosen the best response.1oh....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
 2 years ago
Best ResponseYou've already chosen the best response.1OK. 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
 2 years ago
Best ResponseYou've already chosen the best response.1okay, 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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