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lilsis76 Group Title

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
  • 2 years ago

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  1. satellite73 Group Title
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    looks good to me i never remember the formula, so i set \(2x-\frac{\pi}{3}=0\) and solve for \(x\)

    • 2 years ago
  2. satellite73 Group Title
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    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

    • 2 years ago
  3. lilsis76 Group Title
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    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.

    • 2 years ago
  4. lilsis76 Group Title
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    |dw:1349892894075:dw|

    • 2 years ago
  5. satellite73 Group Title
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    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

    • 2 years ago
  6. satellite73 Group Title
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    hold on, i did not say what you wrote set it equal to zero \[2x-\frac{\pi}{3}=0\] \[2x=\frac{\pi}{3}\] \[x=\frac{\pi}{6}\]

    • 2 years ago
  7. satellite73 Group Title
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    i meant set \[2x-\frac{\pi}{3}=0\] not \[2x-\frac{x}{3}=0\]

    • 2 years ago
  8. lilsis76 Group Title
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    haha okay, i thought = to zero

    • 2 years ago
  9. satellite73 Group Title
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    whew

    • 2 years ago
  10. lilsis76 Group Title
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    haha sorry about that

    • 2 years ago
  11. lilsis76 Group Title
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    okay so to figure the points, i start at pi/6 and move right by pi/6?

    • 2 years ago
  12. satellite73 Group Title
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    lets go slow because i do not want to confuse you

    • 2 years ago
  13. satellite73 Group Title
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    you know \(\cos(0)=1\) right?

    • 2 years ago
  14. lilsis76 Group Title
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    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

    • 2 years ago
  15. satellite73 Group Title
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    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

    • 2 years ago
  16. satellite73 Group Title
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    all you wrote is correct, here is a nice picture http://www.wolframalpha.com/input/?i=+y+%3D+cos+%282x+-+pi%2F3%29+%2B1

    • 2 years ago
  17. lilsis76 Group Title
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    OH! i forgot i have to move it up 1

    • 2 years ago
  18. lilsis76 Group Title
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    okay so then i have it like this: |dw:1349893756732:dw|

    • 2 years ago
  19. lilsis76 Group Title
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    then i move up 1

    • 2 years ago
  20. lilsis76 Group Title
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    |dw:1349893880189:dw|

    • 2 years ago
  21. lilsis76 Group Title
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    @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)

    • 2 years ago
  22. lilsis76 Group Title
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    |dw:1349894136637:dw|

    • 2 years ago
  23. lilsis76 Group Title
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    @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 ) ?

    • 2 years ago
  24. phi Group Title
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    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

    • 2 years ago
  25. lilsis76 Group Title
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    how did you do that?

    • 2 years ago
  26. phi Group Title
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    you know the period is pi, so every time you increase x by pi you will get the same value as x

    • 2 years ago
  27. lilsis76 Group Title
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    sorry, im new to precalculus. all this is super new to me

    • 2 years ago
  28. phi Group Title
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    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

    • 2 years ago
  29. phi Group Title
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    how did you do that? are you asking how to get the lowest point at x= 2/3 pi ?

    • 2 years ago
  30. lilsis76 Group Title
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    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

    • 2 years ago
  31. phi Group Title
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    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?

    • 2 years ago
  32. lilsis76 Group Title
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    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

    • 2 years ago
  33. lilsis76 Group Title
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    |dw:1349897328597:dw|

    • 2 years ago
  34. lilsis76 Group Title
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    this is the graph i got, but i got pi/2 as my lowest. did i do something wrong?

    • 2 years ago
  35. phi Group Title
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    type y = cos (2x - pi/3) +1 in the google search window, it should graph it

    • 2 years ago
  36. lilsis76 Group Title
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    okay im lookin at the graph

    • 2 years ago
  37. lilsis76 Group Title
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    so how do i figure the lowest with that graph?

    • 2 years ago
  38. phi Group Title
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    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

    • 2 years ago
  39. lilsis76 Group Title
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    cos(2x-pi/3) = -1 okay i get this like u did

    • 2 years ago
  40. phi Group Title
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    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?

    • 2 years ago
  41. lilsis76 Group Title
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    i end up getting 2pi/3. and that graph on google is confusing me with different numbers

    • 2 years ago
  42. phi Group Title
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    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...

    • 2 years ago
  43. phi Group Title
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    *The graph shows the curve with x in radians.

    • 2 years ago
  44. lilsis76 Group Title
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    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

    • 2 years ago
  45. phi Group Title
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    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.

    • 2 years ago
  46. lilsis76 Group Title
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    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

    • 2 years ago
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