Is $\sin(x)$ a monotonic function? 
Is $y=\sin(x)$ a  monotonic function?

I want get some idea about the monotonic increase and monotonic decrease include function?
not monotonic function
because wiki said this is not monotonic function.wiki monotonic description
 A: $y=sin x$  is not an monotonic function on $R$.
But $y=sin x$ is monotonic on $[-π/2,π/2]$.
Look at the graph of $y=sin x$ then you can easily figure out whether it is monotonic or not. 
A: No, it is not monotonic. By definition, a monotonic function is one which preserves the order of the real numbers: that is, is $f$ is a function on the real domain or a subset thereof, and we are given two different inputs, one of which precedes the other - that is, if we let the inputs be $a$ and $b$, then $a \le b$, then this precedence is preserved after transforming them by the function, i.e. also $f(a) \le f(b)$ no matter what $a$ and $b$ are so long as both are valid as inputs (i.e. within $\mathrm{dom}(f)$).
So all you nee to ask is "does $\sin(x)$ scramble the order of any two real numbers?" And the answer is yes - take $x = \frac{1}{4} \tau$ and $x = \frac{3}{4} \tau$ (here $\tau = 2\pi$, I prefer this circle constant better) - the two points at which the sine graph reaches its extremes at +1 and -1, respectively, within the first wave cycle. The first point precedes the second, but +1 succeeds -1. The order is changed, and so $\sin(x)$ is not monotonic.
(FWIW, often in a casual calculus context one will hear a function which reverses the order everywhere also called a monotonic function or "monotonic decreasing function", but technically a better term from a theoretician's pov is "anti-monotonic" or "antitonic" function, since this is still a change of order. $\sin(x)$ is not this either because if we go now from $x = \frac{3}{4} \tau$ to $x = \frac{5}{4} \tau$, i.e. going into the next wave cycle, it now goes from -1 to +1, these points are not reversed, so it reverses some but not others, and thus is neither monotonic nor antitonic, but truly order-scrambling.)
