Sine function is periodic function with period of 2pi.
This means that the given sequence will have 12 unique values (because 12cdot pi/6=2pi) and these values will repeat cyclically, more precisely a_n=a_(n+12), forall n in NN. Therefore, we conclude that the given sequence is not monotonic.
On the other hand, codomain of the sine function is [-1,1] so the sequence is obviously bounded.
Maximum terms of the sequence are a_(3+12k)=1, k in ZZ, while the minimum terms are a_(9+12k)=-1, k in ZZ.
The image below shows the first 60 terms of the sequence. We can clearly see the periodic nature of the sequence.
https://en.wikipedia.org/wiki/Sine
Monday, June 3, 2019
a_n = sin(npi/6) Determine whether the sequence with the given n'th term is monotonic and whether it is bounded.
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