Find the Open Interval(s) on Which the Function $f ( x ) = \cos ^ { 2 } ( 3 x )$

Multiple Choice

Find the open interval(s) on which the function $f ( x ) = \cos ^ { 2 } ( 3 x )$ is increasing in the interval Round numerical values in your answer to three decimal places.

A) increasing on: $( 0,0.524 ) , ( 1.047,1.571 ) , ( 2.094,2.618 ) , ( 3.142,3.665 )$
B) increasing on: $( 1.047,0.524 ) , ( 1.047,1.571 ) , ( 2.094,2.618 ) , ( 3.142,4.189 )$
C) increasing on: $( 0.524,1.047 ) , ( 1.571,2.094 ) , ( 2.618,3.142 ) , ( 3.665,4.189 )$
D) increasing on: $( 0,0.524 ) , ( 1.147,1.571 ) , ( 2.094,2.618 ) , ( 3.242,3.665 )$
E) increasing on: $( 1.047,0.524 ) ( 1.047,1.671 ) , ( 2.094,2.618 ) , ( 3.242,4.189 )$