Some help with trig functions (Tangent) please?

Discussion in 'Archived Threads 2001-2004' started by NickSo, Oct 2, 2002.

  1. NickSo

    NickSo Producer

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    okay, i learned Sine/Cosine functions (sine waves and stuff) a few days ago, but last day i learned Tangent.
    I understood the stuff in class "y=tan kx", and i know how to find the period: Pi/|b|
    but i was doing these questions:
    [​IMG]
    I know that "y= A tan B( x - C ) D", where A is the amplitude (vertical stretch for Tan), B affects the period, C is the phase shift, and D is the vertical shift.
    Well, im trying to do the questions above, and it just doesn't make sense when compared to the answers!
    [​IMG]
    #5 is simple, because theres no brackets, but for the other ones, im confused! [​IMG]
     
  2. Rain

    Rain Producer

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    Good grief, I think my brain may explode. [​IMG]
    What have I learned today? That I don't remember a damn thing I learned in High School Math, despite the fact that I had an 89% when I finished. [​IMG]
     
  3. NickSo

    NickSo Producer

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    [​IMG]
    Really, im no slouch in math, i got 93% in Math11, and i did pretty well the first few topics, but this is really screwing me up.
    I have no idea say, for #7 how they came up with a period of Pi/2! Phase shift okay it just says Pi/4, and since its MINUS, i move it to the right.
    But where the hell does the period come from? Theres no number where 'b' is supposda be for the equation of Pi/|b|!
     
  4. Jason Wilcox

    Jason Wilcox Supporting Actor

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    i just started takin calc as a senior in high school. i don't ever remember learning to graph tangent...just cosine and sin...but i think i've got an idea of how it works and the period answer for 7 looks to be a typo....but of course....im not really sure
     
  5. NickSo

    NickSo Producer

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    yeah, im beginning to think so too that theres a typo
     
  6. Jason Wilcox

    Jason Wilcox Supporting Actor

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    i just noticed that there are two number 5's....
     
  7. NickSo

    NickSo Producer

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    yeah, that kinda threw me off as well [​IMG]
     
  8. Denward

    Denward Supporting Actor

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    It's been 20 years since I thought about this stuff but it seems to me that all the questions are of the form y=tan ax+b. Since the period of tan x is pi, then the period of tan ax+b must be pi/|a| (as you stated). Just think of the function as cycling through its possible values a times faster so it must happen over a range that's 1/a times the original period. And then the +b part just shifts the curve left or right so your phase shift is just -b.

    I think the answers look wrong.
     
  9. Artur Meinild

    Artur Meinild Screenwriter

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    Nick, you made a typo in the first formula, it's:
    y = A tan B( x - C ) +
    D
    And let's assume that the "5" in the right column should read "6" instead... [​IMG]
    4 - p: pi/3 , ps: +pi/3
    5 - p: pi/2 , ps: 0 (error in textbook)
    6 - p: pi , ps: -pi/3 (error in textbook)
    7 - p: pi , ps: +pi/4 (error in textbook)
    8 - p: pi , ps: +pi/2
    9 - p: pi/2 , ps: +pi/2 (error in textbook)
    10 - p: 2*pi , ps: -pi (error in textbook)
    11 - p: pi/3 , ps: -pi/9
    It's really unfortunate that there are so many errors in the key, but you will find out that this is sometimes the case. Don't trust the key, trust your logic! [​IMG]
    For example, it's fairly easy to see that 4 and 9 must have answers that look alike, 6, 7 and 8 as well...
     
  10. Dave Morton

    Dave Morton Supporting Actor

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    looks like a typo to me.
     
  11. NickSo

    NickSo Producer

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    NICE! THANK YOU EVERYBODY! I just had about a freakin aneurysm because of it [​IMG]
     
  12. Seth Paxton

    Seth Paxton Lead Actor

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    I thought the period was 2 Pi as Pi is only half a rotation.
    Whoops, nevermind, this is Tangent, not Sin/Cos/Sec/Csc. Takes a few minutes to warm the old brain up for stuff like Trig. [​IMG]
    BTW,
     
  13. Yee-Ming

    Yee-Ming Producer

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    ugh.
    this is depressing, I got an A1 in Maths and A2 in Additional Maths at O-Level, a B in Maths at A-Level, actually taught the stuff for a few months in my old school after I finished school before I entered university, and I can't remember a thing! [​IMG]
     

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