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# What is the period of this function?

f(x)=arctan(tan(x))

Is it periodic at all?

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- DavidLv 68 years agoFavorite Answer
The period is pi.

Why? Because the "inner" function tan(x) controls the periodicity.

If you think that f(x) = x because the functions "cancel", you are wrong, because the arctan function always gives a number between -pi/2 and pi/2.

Graphing f(x), you get a "sawtooth wave" which goes from -pi/2 to pi/2, then drops back to -pi/2, goes back up to pi/2, drops to -pi/2 again, and so on.

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