Give an example, with justification, of a periodic function which is not even.?

2 Answers
Jan 22, 2018

#sin : RR to [-1,1]# has the principal period of #2pi# and is

not even.

Explanation:

#sin : RR to [-1,1]# has the principal period of #2pi# and is

not even.

Jan 22, 2018

#sinx# is not even and has period #2pi# (justified by trigonometric definition)

Explanation:

Here is the graph of #y=sinx#

graph{sinx [-6.786, 7.26, -3.91, 3.113]}

Also the function that returns the fractional part of #x# is periodic, but is neither even nor odd.

We can write that function as

#"frac"(x) = x-lfloorxrfloor#

Note that #"frac"(1/4) = 1/4# and #"frac"(-1/4) = -1/4 - (-1) = 3/4#

So #"frac"(1/4) != "frac"(-1/4)# and #"frac"# is not even.

#"frac"# is periodic with period #1#..

Here is a graph using a different graphing software:

enter image source here