Waves of sine expression

  1. "Waves" of sine expression

    So, I have been working with a lot of Math today(sorry if I am asking so many questions), and I found and expression. All sine functions use radians.

    sin(y) + sin(y) / sin(y)

    Now, assuming you start with 1, if you were to plot y on a graph with variable x increasing each time calculated, you would get something like this:

    [​IMG]

    This image isn't mine, so this is just something identicle.

    Can this be explained?
     
  2. jcsd
  3. Re: "Waves" of sine expression

    Two things.

    First of all, the equation can be simplified. Depending on the use of parentheses, if you mean [itex]\ sin(y)[/itex]+[itex]\frac{ sin(y)}{ sin(y)}[/itex], this simplifies to [itex]\ sin(y)+1[/itex]

    If you meant [itex]\frac{ sin(y)+ sin(y)}{ sin(y)}[/itex], this simplifies to the number 2.

    In the latter case, it is a null statement, but assuming you meant the first equation, the sine function is defined in a couple of cool ways (the easiest being the ratio of the opposite and hypotenuse of a right triangle), and it turns out when you define a function that way it repeats itself like a wave.
     
  4. Re: "Waves" of sine expression

    Thank you for the explanation. I was wondering why it did that(it was obvious, but any who).

    But the expression sin(y) + sin(2*pi) / tan(y) does the same thing. Can that be explained?
     
    Last edited: Mar 9, 2012
  5. HallsofIvy

    HallsofIvy 40,785
    Staff Emeritus
    Science Advisor

    Re: "Waves" of sine expression

    Because [itex]sin(2\pi)= 0[/itex]! And [itex]tan(y)= sin(y)/cos(y)[/itex] so that
    [tex]\frac{sin(y)+ sin(2\pi)}{tan(y)}= \frac{sin(y)}{\frac{sin(y)}{cos(y)}}= sin(y)\frac{cos(y)}{sin(y)}= cos(y)[/tex]
     
  6. Re: "Waves" of sine expression

    And in a more general way, all of the trigonometric functions are periodic, so any combination of trig functions with also be periodic.
     
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