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anonymous

  • 5 years ago

How do I find the period of this function? y= -2sec(x+(pi/4))

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  1. amistre64
    • 5 years ago
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    the period of the function is whatever is multiplying your "x" and something with 2pi...

  2. amistre64
    • 5 years ago
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    since nothing is affecting your x...like say: sec(3x).. then it is a normal period

  3. anonymous
    • 5 years ago
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    I don't understand it. How you go about doing it?

  4. amistre64
    • 5 years ago
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    with this problem, there is nothing to demonstrate... but in general: asin(p(x+sh)) are your important point. a = amplitude sh = horizontal shift p = period and when p is not 1; yor period become: normal period ----------- p

  5. amistre64
    • 5 years ago
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    lets take: cos(5x) the normal period for cos is 2pi the period for this setup here would be: 2pi ---- 5

  6. anonymous
    • 5 years ago
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    Can you please show me how to do it with this problem? I 'm so confused.

  7. amistre64
    • 5 years ago
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    Here is the problem you gave us..make sure its correct and that you havent left anything out... y= -2sec(x+(pi/4))

  8. anonymous
    • 5 years ago
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    Yeah, it's right.

  9. amistre64
    • 5 years ago
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    ok... can you tell me what the -2 in front of it means?

  10. amistre64
    • 5 years ago
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    if you dont know, just give it your best shot

  11. anonymous
    • 5 years ago
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    That's the amplitude, right? Other than that I don't know what it means.

  12. amistre64
    • 5 years ago
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    that is correct...amplitude is a fancyname for saying: This is how high or low I can go. can you tell me what the "sec" part means?

  13. anonymous
    • 5 years ago
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    Sec is 1/x if x=0

  14. amistre64
    • 5 years ago
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    good... but a more accurate definition is: 1/cosine all the trig functions have a name, and the name of that function just tells us how to solve for certain parts of a triangle really... now what can you tell me about the inside of the sec function? what does it mean to you?

  15. amistre64
    • 5 years ago
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    if sec(x) is when everything is normal.... what have they done to it?

  16. anonymous
    • 5 years ago
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    This is where I get confused.

  17. anonymous
    • 5 years ago
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    They haven't done anything to it, right?

  18. amistre64
    • 5 years ago
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    ill step you thru it :) take your best shot.... when they mess with the normal stuff inside the function, what are they doing?

  19. anonymous
    • 5 years ago
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    Changing its degree or shift to a different quadrant. THANKS SO MUCH BTW :)

  20. amistre64
    • 5 years ago
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    thats right :) good job

  21. amistre64
    • 5 years ago
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    think of the inside of that function as you trying to aim an arrow at the x line.... does this help?

  22. amistre64
    • 5 years ago
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    when things are normal inside there, you will hit the "x" everytime... but when things start to get played with and moved around, your aim gets off

  23. anonymous
    • 5 years ago
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    You are trying to move across it or go above or below it.

  24. amistre64
    • 5 years ago
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    that is correct... now there are 2 ways that they can miss up our aim, by adding stuff or multiplying stuff. each way has a specific affect on our aim...

  25. anonymous
    • 5 years ago
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    would the answer be 2pi/-2

  26. amistre64
    • 5 years ago
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    nope.... the -2 already played its part, it told us how far to strech the graph up and down.... it doesnt mess with the period or the "phase shift".

  27. amistre64
    • 5 years ago
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    when we ADD stuff inside the function it moves us around..left or right.... it shifts us left or right....

  28. anonymous
    • 5 years ago
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    would i have to divide 2pi/ (pi/4) which i did but was not right

  29. amistre64
    • 5 years ago
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    Not quite... the pi/4 is ADDED to x so it only moves everything left or right.... its called a "shift"

  30. anonymous
    • 5 years ago
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    so pi/4x?

  31. amistre64
    • 5 years ago
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    we change the "period" my muliplying or dividing the inside of the function.....

  32. anonymous
    • 5 years ago
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    how do we do that though? what do we multiply or divide it by?

  33. amistre64
    • 5 years ago
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    can you tell me what a period is in relation to a trig function?

  34. amistre64
    • 5 years ago
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    what does the period of a function tell us?

  35. anonymous
    • 5 years ago
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    It shows how far the function can move up and down in the y-direction.

  36. amistre64
    • 5 years ago
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    not quite, that would be the "vertical" shift... that is not the period. think along the lines of "how long it takes to go thru 1 complete cycle". the graph looks like a wave..usually... and that wave goes up then comes down...then goes under...then comes back to the x axis.... after 1 complete cycle, it has to start over again... does that make sense?

  37. anonymous
    • 5 years ago
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    Kind of, isn't a complete cycle 2pi? So every time it hits the x-axis it begins a new cycle?

  38. amistre64
    • 5 years ago
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    a complete cycle..or period... for the sin and cos function is 2 pi, that is correct. But remember the graphs of these things if you can. they hit the x line twice, in one cycle. A NEW cycle begins when they are back to their original starting place and have to go thru the motions again. It is like a spinning wheel, every time the wheel makes 1 complete turn, it has gone thru 1 period.

  39. anonymous
    • 5 years ago
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    I understand that, but still confused on how to go on with the problem?

  40. anonymous
    • 5 years ago
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    Can I substitute 0 in for x and solve from there?

  41. amistre64
    • 5 years ago
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    ok.... The period is affected when they "multiply" or "divide" that X buy a number. that number tells the graph to speed up along it period or to slow down and draw out its period... the inside of your function here is: (x + pi/4) Is there a number that is multiplying the "x"?

  42. anonymous
    • 5 years ago
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    yes

  43. amistre64
    • 5 years ago
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    im here :)

  44. anonymous
    • 5 years ago
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    i'm ready

  45. amistre64
    • 5 years ago
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    ok.... now as I was on break.... I was thinking aboout what it is you might be asking for with this problem. Are you sure it is the "period" that you want to find? Or is it the values that the period is in, like pi/4 to 8pi/4 like that?

  46. anonymous
    • 5 years ago
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    Yeah, on my homework it asks me to find the period of the function.

  47. amistre64
    • 5 years ago
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    then ill continue as before..... the period of the function. Now, you said that there was a number that was "multiplying" the inside of our function: (x+ pi/4) what number do you see that is multiplying this?

  48. amistre64
    • 5 years ago
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    ill give you a hint, if there is a number multiplying this function it would be standing in fronnt of our "x"

  49. anonymous
    • 5 years ago
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    x is multiplying i think

  50. anonymous
    • 5 years ago
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    the sec?

  51. amistre64
    • 5 years ago
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    the sec is the name of our function, not a multiplier....

  52. amistre64
    • 5 years ago
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    is there a number in front of our x? ( ___ x+ pi/4) ^ is there a number right here in this spot?

  53. anonymous
    • 5 years ago
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    no

  54. amistre64
    • 5 years ago
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    lol.....good job :) since there is no number there, our period is normal. the normal period for a sec function is 2pi

  55. amistre64
    • 5 years ago
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    what if there had been a number there, how would we have found the period of this function? do you know?

  56. anonymous
    • 5 years ago
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    I was about to ask the same thing lol We would have to multiply the number by 2pi, wrong?

  57. amistre64
    • 5 years ago
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    divide.... think divide. the period would be equal to: 2pi ------- number

  58. anonymous
    • 5 years ago
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    So for example: If the number was 3x, we would divide 2pi/3

  59. amistre64
    • 5 years ago
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    that is correct.....

  60. amistre64
    • 5 years ago
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    now remember, the tan and cot have a normal period of just "pi".... so that would be the top when you have to deal with those

  61. anonymous
    • 5 years ago
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    So if there is no number then the answer is just 2pi?

  62. amistre64
    • 5 years ago
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    correct, no number is just 2pi..... or if the function is a tan or cot... its just pi

  63. anonymous
    • 5 years ago
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    Does it matter if the degrees are the different? Such as what if it was -2sin?

  64. amistre64
    • 5 years ago
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    -2sin(x) has a period of 2pi since there is no number in front of our x value.

  65. amistre64
    • 5 years ago
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    just aim into the inside of the function, and forget everything else around it....

  66. anonymous
    • 5 years ago
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    Ok, is possible for you to help me with one more?

  67. amistre64
    • 5 years ago
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    maybe.... whatcha got?

  68. anonymous
    • 5 years ago
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    y= 1/10tan(pi(x)-pi)

  69. amistre64
    • 5 years ago
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    good, I take it that that is (1/10) tan..... or is that tan supposed to be under the fraction ?

  70. anonymous
    • 5 years ago
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    (1/10)tan

  71. amistre64
    • 5 years ago
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    ok.... so whats our question for this one?

  72. anonymous
    • 5 years ago
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    Same one, find the period for this function?

  73. amistre64
    • 5 years ago
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    recall what the normal period for the tan function is.... do you remember it? is it 2pi or pi ?

  74. anonymous
    • 5 years ago
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    yeah, so i would have to divide 2pi/pi in this case

  75. anonymous
    • 5 years ago
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    i'm sorry pi

  76. amistre64
    • 5 years ago
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    youve got the right idea.... but first we need to know what the normal period for the tan function is....

  77. anonymous
    • 5 years ago
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    pi/pi then?

  78. amistre64
    • 5 years ago
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    yes...very good :)

  79. anonymous
    • 5 years ago
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    the answer would be 1 then?

  80. amistre64
    • 5 years ago
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    yep, it repeats itself after every 1.

  81. amistre64
    • 5 years ago
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    instead of repeating at every 3.14; it repeats itself here ate every 1

  82. anonymous
    • 5 years ago
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    so for this problem y= -7sec(x) the answer would be 2pi

  83. amistre64
    • 5 years ago
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    thats correct :)

  84. anonymous
    • 5 years ago
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    got it. you are so much better than my professor. THANK YOU SO MUCH!!!

  85. amistre64
    • 5 years ago
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    lol .... maybe :) youre welcome

  86. anonymous
    • 5 years ago
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    No, believe you are :)

  87. anonymous
    • 5 years ago
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    me*

  88. amistre64
    • 5 years ago
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    ive just got more time to devout to teaching it.... but thanx :)

  89. anonymous
    • 5 years ago
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    for y= sec(2x+(3pi/2)) would the answer be 2pi/2x= 3.14x

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