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
To find the period of the function given in the question:
Let's say =
Now,
Since, the greatest integer function will give the output of as -1, 0, 1 but the period will be similar to sin 3x.
Hence, Period of is
Now,
Since, modulus always give a positive output, hence the output of will be 0,1, thus the output will repeat after every interval of
Hence,
Therefore, Period of is
Thus, the period of the composite function = will be the LCM of and
or,
Thus, period of is
Hope this information will clear your doubts about the topic.
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The period of each sin x and cos x is
To find the period of the function given in the question:
Let's say =
Now,
Since, the greatest integer function will give the output of as -1, 0, 1 but the period will be similar to sin 3x.
Hence, Period of is
Now,
Since, modulus always give a positive output, hence the output of will be 0,1, thus the output will repeat after every interval of
Hence,
Therefore, Period of is
Thus, the period of the composite function = will be the LCM of and
or,
Thus, period of is
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.
Regards