Find the period of the function [sin3x] +
|cos6x| , where [] is greatest integer function and | | denotes modulus function . Answer is 2π/3

Dear Student,

The period of each sin x and cos x is 2π
To find the period of the function given in the question:

Let's say sin 3x+cos 6x=Px+Qx

Px=sin 3x=sin 3x+2π=sin 3x+2π3
Since, the greatest integer function will give the output of Px=sin 3x as -1, 0, 1 but the period will be similar to sin 3x.
Hence, Period of Px=sin 3x is 2π3
Qx=cos 6x
Since, modulus always give a positive output, hence the output of cos x will be 0,1, thus the output will repeat after every interval of π
Qx=cos 6x=cos 6x+π=cos 6x+π6
Therefore, Period of Qx=cos 6x is π6
Thus, the period of the composite function Px+Qxsin 3x+cos 6x will be the LCM of 2π3 and π6
Thus, period of sin 3x+cos 6x is 2π3

Hope this information will clear your doubts about the topic.

If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.


  • 5
What are you looking for?