Is Sin n a Non-Monotonic Function?

[garyljc]

i understand that non monotonic is neither decreasing nor increasing
does it mean sin n is also non monotonic ?

 

[Ed Aboud]

As a whole the function is not monotonic, but say if you consider the interval between 0 and pi/2 it is increasing. Hope that helps.

 

[HallsofIvy]

i understand that non monotonic is neither decreasing nor increasing
does it mean sin n is also non monotonic ?

A non-monotonic function is neither always decreasing nor always increasing.

Yes, sin(x) is a non-monotonic function. If You intended n to be an integer, sin n is still non-monotonic because sin(0)= 0 and sin(1)= .8414... so it is increases from 0 to 1 but sin(2) is .9092... and sin(3)= .1411... so it decreases from 2 to 3.

As Ed Aboud said, you can restrict it to some intervals on which it is monotonic, but, strictly speaking, that gives a different function.