Give an example of an odd function, other than f (x) = 0, for which f (x) = f (x+4π).

... I just found the answer sin (x + 4π) = sinx - but it was a random guess, and i cant explain my reasoning ... i know that sin is an odd function as sin (-x) = - sin (x) - but thats about it.

Question

Mathematics

Cecilia Whitehead

26 November, 19:56

Give an example of an odd function, other than f (x) = 0, for which f (x) = f (x+4π).

... I just found the answer sin (x + 4π) = sinx - but it was a random guess, and i cant explain my reasoning ... i know that sin is an odd function as sin (-x) = - sin (x) - but thats about it.

+1

Answers (1)

Know the Answer?

Marco Dawson · Answer 1

f (x) = f (x+4π) is a periodic function with the period of 4π

Since sinx has a period of 2π, you can write f (x) = f (x+2π) = f (x+4π) ...

Another example of odd function : f (x) = tan x

Give an example of an odd function, other than f (x) = 0, for which f (x) = f (x+4π).... I just found the answer sin (x + 4π) = sinx - but it was a random guess, and i cant explain my reasoning ... i know that sin is an odd function as sin (-x) = - sin (x) - but thats about it.

Give an example of an odd function, other than f (x) = 0, for which f (x) = f (x+4π).

... I just found the answer sin (x + 4π) = sinx - but it was a random guess, and i cant explain my reasoning ... i know that sin is an odd function as sin (-x) = - sin (x) - but thats about it.