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Sin/cos/tan graphs

  1. Mar 15, 2014 #1
    I know the general equation for trig functions and how to manipulate them:
    y=A sin [B (x-c)] + D
    howver , the tan function has a period of ∏/b. how is this derived? I know it has to do with tan = y/x right? but I just don't understand how to derive the period when you're graphing a tan function.

    Thanks,
    Randy
     
  2. jcsd
  3. Mar 15, 2014 #2

    micromass

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    You're asking about the function ##f(x) = \tan(x)##? Then what is ##b##?

    Also, how did you define the tangent function?
     
  4. Mar 15, 2014 #3

    Mark44

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    In addition to what micromass said, "tan = y/x" is not correct. There's an angle involved that you don't show. Tangent of what? It's a little like saying "√ = 4". Square root of what?
     
  5. Mar 15, 2014 #4
    hmmm...maybe I'm not being clear. If using the "unit circle" the sin function is y/r, cos is x/r, tan is y/x, where r=1. Is this not how you plot a sin/cos/tan function on the x/y plane?
     
  6. Mar 15, 2014 #5

    micromass

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    Well first of all, if you take a unit circle definition, then I don't see why you bother to write the ##r##.

    Second, you ignored the post by Mark. There is no such thing as a ##\tan##. You need to take the ##\tan## of some angle.

    Anyway, let's move on to you question. You know that

    [tex]\tan(x) = \frac{\sin(x)}{\cos(x)}[/tex]

    holds for all ##x## for which the fraction on the right is defined.
    Can you try to show that

    [tex]\tan(x+\pi) = \tan(x)[/tex]

    To do this, do you know some formulas for ##\sin(x+\pi)## and ##\cos(x+\pi)##?
     
  7. Mar 16, 2014 #6
    tan(x) formula

    I'm sorry, but I don't see how this is germane to a tan function. In a standard problem that asks to A:graph a tangent function B:show the period of the function C: show the asymptotes D: give the domain and range. I don't see how the formulas [tex]\sin(x+\pi)[/tex] and [tex]\cos(x+\pi)[/tex] help me get there.

    Thanks
     
  8. Mar 16, 2014 #7

    micromass

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    Seeing as this is a standard problem, I moved it to the homework forums. Now, please provide an attempt at solving the problem before we can continue.
     
  9. Mar 16, 2014 #8
    graph tan(4t)

    ok. here is one I missed. graph [tex] y= tan(4t) [/tex]
    A: find the period.
    B: find the phase shift
    c: give the domain/range
    d: find the asymptotes
    the general formula for the tan/cot funcit is [tex] y= A tan [B (x-C)] + D [/tex]. A is amp, [tex] ∏/B [/tex] is the period, [tex] C [/tex] will give the phase shift, and [tex] D [/tex] is the vertical translation.
    I know that at the points on the unit circle (0,1) and (0,-1) the function is UNDEFINED, so this is the asymptote. Now WHAT IS THE [tex] 4t [/tex]? This is what I missed.
    Thanks,
     
  10. Mar 17, 2014 #9
    ##4t## is your independent variable, instead of an ##x## or ##\theta## that you might usually see. You can use this 4t to find the period of this particular function. ##tan\theta## contains a period of ##\pi## but since you're dealing w/ ##tan(n\theta##), your period will be ##\frac{\pi}{n}## which will give you a ratio of ##\pi## relative to your function, in other words n(##\frac{\pi}{n}##) = ##\pi##
     
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