"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: This image isn't mine, so this is just something identicle. Can this be explained?
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.
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?
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]
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.