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12 pi

Multiplying 'x' by a fraction < 1  stretches the function out.......multiplying 'x' by a number > 1 shortens the period.

( take 2 pi and divide by the number that x is multiplied by to get the period

     example   cos 1/6 x    has a period of   2 pi /(1/6) = 12 pi

     example    cos 3x       has a period of    2pi/3

sin [ (1/6) x ]

We have the form

sin [ bx ] 

In this form , the period can be found as

2 pi / b

So we have :

period   =   2pi / (1/6)  =  2pi * 6/1   =    12 pi